8.3 and 8.4 Trigonometric Ratios
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Transcript of 8.3 and 8.4 Trigonometric Ratios
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30⁰
8.3 and 8.4 Trigonometric Ratios
Finding Trig Ratios
• A trig ratio is a ratio of the lengths of two sides of a right triangle.
• The word trigonometry is derived from the ancient Greek language and means measurement of triangles.
• The three basic trig ratios are sine, cosine, and tangent.
• Abbreviated as sin, cos, and tan respectively
Trigonometric Ratios
• Let ∆ABC be a right triangle. If you are standing from angle A, the following sides are labeled: opposite, adjacent and hypotenuse
ac
bside adjacent to angle A
Sideoppositeangle A
hypotenuse
A
B
C
sin A =opposite
hypotenuse=
a
c
cos A = adjacent
hypotenuse=
b
c
tan A =opposite
adjacent =
a
b
Trigonometric Ratios
• If you were standing at angle B, you would have to re-label the sides of opposite, adjacent and hypotenuse
sin B =opposite
hypotenuse=
b
c
cos B = adjacent
hypotenuse=
a
c
Tan B =opposite
adjacent =
b
a
ac
bside opposite to angle B
Sideadjacentangle B
hypotenuse
A
B
C
The famous Indian…
SOHCAHTOA
Ex. 1: Find sin, cos and tan of angle S
Ratio S
sin S = opposite
hypotenuse
cosS = adjacent
hypotenuse
tanS = opposite
adjacent 12
13 5
R
T S
Ex.2: Find the sin, cos and tan of angle R
Ratio R
sin R = opposite
hypotenuse
cosR= adjacent
hypotenuse
tanR = opposite
adjacent
12
13 5
R
T S
Using the Inverse
• You can use the sin, cos and tan ratio and calculate it’s inverse, sin-1, cos-1, tan-1 to find the measure of the angle.
• Make sure your calculator is in degree mode!!!
*make note: sin, cos, and tan are ratios.Inverses find angles!!!
Let’s find angle S.
Ratio S
sin S = opposite
hypotenuse
cosS = adjacent
hypotenuse
tanS = opposite
adjacent 12
13 5
R
T S
Now let’s find the angle measure from a previous example
Ratio R
sin R = opposite
hypotenuse
cosR= adjacent
hypotenuse
tanR = opposite
adjacent
12
13 5
R
T S
Examples: Given the triangles below, find the missing angle measure to the nearest degree
26
?
6
8
10 ?
Practice: Solve for the missing variables
1.) 2.)
3.) 4.)
x⁰
12
16
7
26⁰ m
40⁰
9
yz
30
15
(No decimal answers in 4)
p