Find the missing measures. Write all answers in radical form. 60° 30° 10 y z Warm – up 3 45 y...
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Transcript of Find the missing measures. Write all answers in radical form. 60° 30° 10 y z Warm – up 3 45 y...
Find the missing measures. Write all answers in radical form.
60°
30° 10
y
z
Warm – up
3
45y60
30x
45
23
33
y
x
5
35
y
z
Math II
UNIT QUESTION: What patterns can I find in right triangles?Standard: MM2G1, MM2G2
Today’s Question:What is a trigonometric ratio?Standard: MM2G2.a,b
The Trigonometric Functions we will be
looking at
SINE
COSINE
TANGENT
5.2 & 5.3
The Trigonometric Functions
SINE
COSINE
TANGENT
SINE
Pronounced “sign”
Pronounced “co-sign”
COSINE
Pronounced “tan-gent”
TANGENT
Prounounced “theta”
Greek Letter
Represents an unknown angle
oppositehypotenuse
SinOpp
Hyp
Leg
adjacent
CosAdj
Hyp
Leg
TanOpp
Adj
Leg
Leg
hypotenuseopposite
adjacent
We need a way to remember all of these ratios…
Old Hippie
Old Hippie
SomeOldHippieCameAHoppin’ThroughOurApartment
SOHCAHTOA
Old Hippie
Old Hippie
SinOppHypCosAdjHypTanOppAdj
Or there’s the famous Indian Chief,
Chief SOH CAH TOA
Sin = Opp/HypCos = Adj/HypTan = Opp/Adj
Finding sin, cos, and tan.
(Just writing a ratio or decimal.)
Find the sine, the cosine, and the tangent of angle A.
Give a fraction and decimal answer (round to 4 places).
hyp
oppA sin
8.10
9 8333.
hyp
adjA cos
8.10
6 5556.
adj
oppA tan
6
9 5.1
9
6
10.8
A
Shrink yourself down and stand where the angle is.
Now, figure out your ratios.
Find the sine, the cosine, and the tangent of angle A
A
24.5
23.1
8.2
hyp
oppA sin
5.24
2.8 3347.
hyp
adjA cos
5.24
1.23 9429.
adj
oppA tan
1.23
2.8 3550.
Give a fraction and decimal answer (round to 4 decimal places).
Shrink yourself down and stand where the angle is.Now, figure out your ratios.
Finding an angle.(Figuring out which ratio to use and getting
to use the 2nd button and one of the trig buttons.)
Ex. 1: Find . Round to four decimal places.
9
17.2
Make sure you are in degree mode (not radians).
9
2.17tan
2nd tan 17.2 9
3789.62
)
Shrink yourself down and stand where the angle is.Now, figure out which trig ratio you have and set up the problem.
Ex. 2: Find . Round to three decimal places.
23
7
Make sure you are in degree mode (not radians).
23
7cos
2nd cos 7 23
281.72
)
Ex. 3: Find . Round to three decimal places.
400
200
Make sure you are in degree mode (not radians).
400
200sin
2nd sin 200 400
30)