EOL: Trigonometry … · Trigonometry Vocabulary: Right angle triangle, hypotenuse, opposite side,...
Transcript of EOL: Trigonometry … · Trigonometry Vocabulary: Right angle triangle, hypotenuse, opposite side,...
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solveproblems that involve Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
TrigonometryApplication Math 2
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solve problems that involve Pythagoras’ Theorem and the Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solveproblems that involve Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Trigonometry
• We can use trigonometry to find missing angles and lengths of triangles.
• Trigonometry uses three functions, these are called:• Sine (shortened to Sin and pronounced “sign”)
• Cosine (shortened to Cos)
• Tangent (shortened to Tan)
• We will start working with right angled triangles
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solve problems that involve Pythagoras’ Theorem and the Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solveproblems that involve Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Labelling the sides
The longest side, the one opposite the
right angle is called the hypotenuse
Before we can use Sin, Cos and Tan we need to be able to label the sides of a right angled
triangle
Trigonometry
Labelling the sides
Op
po
site
The name of the other two sides will change depending on
which angle we are working with, for example..
ϴ
Adjacent
If we are given (or need to work out) this
angle, we label the other sides like this..
But if we are
working with this
angle, we label the
sides like this...
Opposite
Ad
jace
nt
Trigonometry
OppositeAdjacent
Hypotenuse
A) B)
C)
ϴX
What is the side marked with an X?
Trigonometry
Adjacent
Hypotenuse OppositeA) B)
C)
ϴ
X
What is the side marked with an X?
Trigonometry
Hypotenuse Opposite
Adjacent
A) B)
C)
ϴ
X
What is the side marked with an X?
Trigonometry
Opposite Adjacent
Hypotenuse
A) B)
C)
ϴ
X
What is the side marked with an X?
Trigonometry
Hypotenuse
Adjacent OppositeA) B)
C)
ϴX
What is the side marked with an X?
Trigonometry
AdjacentOpposite
Hypotenuse
A) B)
C)
ϴX
What is the side marked with an X?
Trigonometry
AdjacentOpposite
Hypotenuse
A) B)
C)
ϴ
X
What is the side marked with an X?
Trigonometry
Opposite Hypotenuse
Adjacent
A) B)
C)
ϴ
What is the side marked with an X?
Trigonometry
Opposite
Hypotenuse AdjacentA) B)
C)
ϴ
X
What is the side marked with an X?
Trigonometry
Hypotenuse Opposite
Adjacent
A) B)
C)
ϴ
X
What is the side marked with an X?
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solve problems that involve Pythagoras’ Theorem and the Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solveproblems that involve Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Sine (sin)
𝜃˚O
pp
osi
te
We use Sine ratio when we have the Oppositelength and the Hypotenuse
The Ratio we use is:
Sin𝜃 =𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solve problems that involve Pythagoras’ Theorem and the Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solveproblems that involve Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Sin Example 1
42˚𝑥
We can use Sin as the question involves the Opposite length and the Hypotenuse
The Ratio we use is:
Sin𝜃 =𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
Sin42° =𝑥
7
7 x Sin42° = 𝑥
4.68𝑐𝑚 (2. 𝑑𝑝) = 𝑥
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solve problems that involve Pythagoras’ Theorem and the Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solveproblems that involve Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Sin Example 1
17˚
10𝑐𝑚
We can use Sin as the question involves the Opposite length and the Hypotenuse
The Ratio we use is:
Sin𝜃 =𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
Sin17° =10
𝑥
𝑥Sin17° = 10
𝑥 =34.2 ( 1 dp)
𝑥 =10
𝑆𝑖𝑛17
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solve problems that involve Pythagoras’ Theorem and the Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solveproblems that involve Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Cosine (cos)
𝜃 ˚
Adjacent
We use cosine when we have the Adjacentlength and the Hypotenuse
The Ratio we use is:
𝐶𝑜𝑠𝜃 =𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solve problems that involve Pythagoras’ Theorem and the Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solveproblems that involve Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Cosine Example 1
53˚
𝑥
We can use Cosine as the question involves the Adjacent length and the Hypotenuse
The Ratio we use is:
Cos53° =𝑥
9
9 x Cos53° = 𝑥
5.42𝑐𝑚(2 𝑑𝑝) = 𝑥
𝐶𝑜𝑠𝜃 =𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solve problems that involve Pythagoras’ Theorem and the Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solveproblems that involve Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Cosine Example 2
We can use Cosine as the question involves the Adjacent length and the Hypotenuse
The Ratio we use is:
Cos26° =8
𝑥
𝑥Cos26° = 8
𝑥 = 8.9 ( 1 dp)𝑥 =
8
𝐶𝑜𝑠26
𝐶𝑜𝑠𝜃 =𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
26˚
8 c
m
x
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solve problems that involve Pythagoras’ Theorem and the Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solveproblems that involve Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Tangent (tan)
𝜃˚
AdjacentO
pp
osi
te
We use Tangent when we have the Oppositelength and the Adjacent
The Ratio we use is:
Tan𝜃 =𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solve problems that involve Pythagoras’ Theorem and the Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solveproblems that involve Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Tangent Example 1
We can use Tangent as the question involves the Adjacent length and the Opposite
The Ratio we use is:
Tan 53° =𝑥
11
11 x Tan53° = 𝑥
14.6𝑐𝑚(1 𝑑𝑝) = 𝑥
53˚
11𝑐𝑚𝑥
Tan𝜃 =𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solve problems that involve Pythagoras’ Theorem and the Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solveproblems that involve Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Tangent Example 2
We can use Tangent as the question involves the Adjacent length and the Opposite
The Ratio we use is:
Tan35° =21
𝑥
𝑥Tan35° = 21
𝑥 = 30cm ( 1 dp)𝑥 =
21
𝑇𝑎𝑛35
Tan𝜃 =𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡
35˚
x2
1cm
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solve problems that involve Pythagoras’ Theorem and the Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solveproblems that involve Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Sin𝜃 =𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
Tan𝜃 =𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡
𝑪𝑜𝑠𝜃 =𝑨𝑑𝑗𝑎𝑐𝑒𝑛𝑡
𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
SOH
CAH
TOA
Trigonometry Ratio
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solve problems that involve Pythagoras’ Theorem and the Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solveproblems that involve Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Selecting Ratio
10cm
63o
x
sinѲ =
sin63 =
x = 10sin63
x = 8.91cm (2dp)
OppositeHypotenuse
x10
S O H
C A H
T 0 A
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solve problems that involve Pythagoras’ Theorem and the Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solveproblems that involve Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
9cm
49o
x
CosѲ =
Cos49 =
x = 9cos49
x = 5.90 cm (2dp)
AdjacentHypotenuse
x9
S O H
C A H
T 0 A
Selecting Ratio
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solve problems that involve Pythagoras’ Theorem and the Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solveproblems that involve Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
12cm
52o
x
TanѲ =
Tan52 =
x = 12Tan52
x = 15.26 cm (2dp)
OpppositeAdjacent
x12
S O H
C A H
T 0 A
Selecting Ratio
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solve problems that involve Pythagoras’ Theorem and the Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solveproblems that involve Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Determine the value of the unknown
x
7cm
35o
SOH CAH TOA
x = 4.90 cm (3 s.f.)
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solve problems that involve Pythagoras’ Theorem and the Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solveproblems that involve Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
10cm
40o
SOH CAH TOA
Determine the value of the unknown
p = 15.6 cm (3 s.f.)
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solve problems that involve Pythagoras’ Theorem and the Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solveproblems that involve Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
20cm
35o
SOH CAH TOA
Determine the value of the unknown
w = 24.4 cm (3 s.f.)
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solve problems that involve Pythagoras’ Theorem and the Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solveproblems that involve Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
9 cm
y47o
Determine the value of the unknown
y = 6.14 cm (3 s.f.)
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solve problems that involve Pythagoras’ Theorem and the Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
Trigonometry
Vocabulary: Right angle triangle, hypotenuse, opposite side, adjacent side, angle
EOL: Given 5 problems that involve trigonometry students will solve with an accuracy of at least 80%
LO: Students will solveproblems that involve Trigonometry Ratios
Agenda:
1. Do Now2. Discussion of Do Now3. Recap Previous lesson4. Instructional Activity5. Guided Practice6. Individual work7. Closure
z
13
55o
SOH CAH TOA
Determine the value of the unknown
Z = 9.10 cm (3 s.f.)
Trigonometry
Finding Missing Angle - Sine
ϴ
4cm
Trig. Ratios can be used to find missing angle(ϴ)
Sin𝜃 =𝑶𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
Sin𝜃 =𝟒
𝟓
Sin𝜃 = 0.800 (3 𝑠𝑓)
Sin𝜃 = 0.800 (3 𝑠𝑓)
𝜃 = 𝑆𝑖𝑛−1(0.800
𝜃 = 53.1°
Trigonometry
Finding Missing Angle - Cos
Trig. Ratios can be used to find missing angle(ϴ)
Cos𝜃 =𝑨𝑑𝑎𝑐𝑒𝑛𝑡
𝑯𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
Cos𝜃 =3
𝟓
Cos𝜃 = 0.600 (3 𝑠𝑓)
Cos𝜃 = 0.600 (3 𝑠𝑓)
𝜃 = 𝐶𝑜𝑠−1(0.600
𝜃 = 53.1°
ϴ3cm
Trigonometry
Finding Missing Angle - Tan
Trig. Ratios can be used to find missing angle(ϴ)
Tan𝜃 =𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑨𝑑𝑎𝑐𝑒𝑛𝑡
Tan𝜃 =4
3
𝜃 = 𝑇𝑎𝑛−1(4
3)
𝜃 = 53.1°
ϴ
4cm
3cm
Trigonometry
Trig Ratios
Sine Ratio:
SinѲ =
Cosine Ratio:
CosѲ =
Tangent Ratio:
TanѲ = Opposite
HypotenuseAdjacent
HypotenuseOppositeAdjacent
Hypotenuse
Opposite
Hypotenuse
Adjacent
Ad
jace
nt
Opposite
SOH CAH TOA
Trigonometry
Trigonometry
17cma cm
27o
Ѳ
15cm
9cm
11m38o
b m
10cm
14cm
𝜃
c cm
21cm
71𝑜
d cm
11cm
84𝑜