1. 9-2 Sine and Cosine Ratios
5/1/17
9-2 Sine and Cosine Ratios
Objective: To use sine and cosine to determine side lengths in right triangles.
SINE A : opposite
hypotenuse
COSINE A: adjacent C
Hypotenuse
Opposite A B
Adjacent

2. sin x = cos y Ex: Use the triangle to write each ratio:
sin T = opp = G
hyp 17
cos T = adj =
hyp
sin G = opp = 15
hyp T R
cos G = adj = 8
Write sine and cosine ratios for x and y x 48
z y
In general, how are sin x and cos y related?
Yes these should be reduced. The original triangle is what pyth. triple?
sin x = 64 80
cos x = 48 80 80
sin y = 48 80
cos y = 64 80
3-4-5 (times 16)
sin x = cos y

3. sin xo = cos (90 – x)o for values of x between 0 and 90 L
IDENTITY:
sin xo = cos (90 – x)o for values of x between 0 and 90 L
Ex: Find m L to the nearest degree
a) Using cos b) using sin
cos L = 2.5 = sin L = 3.1
F O
m L = cos-1 (5/8) m L = sin-1 (3.1/4.0)
= = 51
Find the value of x to the nearest degree
1) ) 10 xo xo
m x = cos-1 (10/27)
= cos-1 (.370)
m x = sin-1 (6.5/10)
= sin-1 (.65)
= 68°
= 41°

4. sin A = 16 34
sin B = 30 34
Yes these should be reduced. The original triangle is what pyth. triple? B 16
C A
Write the ratios for sin A and sin B
Write the ratios for cos A and cos B
L x K y
57o 25 M
Find x to the nearest tenth
Find y to the nearest tenth 34
(times 2)
cos A = 30 34
cos B = 16 34
sin 57 = x 25
x = 25•sin 57 = 21.0
cos 57 = y 25
y = 25•cos 57 = 13.6

5. BTW this triangle was what triple?
Assignment: Page 479 #1 – 17, 25, 31, 33
BTW this triangle was what triple? N x 60 y
P R
Find x to nearest degree
Find y to nearest degree
m x = sin-1 (63/87)
= 46° 87
m y = sin-1 (60/87)
= 44°
Make sure the calc is in DEGREE mode!!!!