18. Given that sin x = 8 and sin y = , where x and y are acute, find the value of cos (x + y). 17 A. B. 130 221 140 221 140 204 220 22 C. D.

asked Aug 14, 2023 13.2k views

8 votes

18.

Given that sin x =
8
and sin y = , where x and y are acute, find the value of cos (x + y).
17
A.
B.
130
221
140
221
140
204
220
22
C.
D.

4.3k points

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11 votes

Answer:

Explanation:

$sin(x)=(5)/(13), cos(x)=\sqrt{1-((5)/(13))^2}=(12)/(13)$

$sin(y)=(8)/(17), cos(y)=\sqrt{1-((8)/(17))^2}=(15)/(17)$

$\cos(x+y)=cos(x)cos(y)-sin(x)sin(y)\\=(12)/(13)*(15)/(17)-(5)/(13)*(8)/(17)\\=(140)/(221)$

Amrrs answered Aug 19, 2023

by Amrrs

4.2k points

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