Answered

Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

If a and b are two angles in standard position in Quadrant I, find cos(a-b) for the given function values. sin a=3/5and cos b=12/37

1) 153/185

2) 57/185

3) -57/185

4) -153/185

(Use the sum of identity for cosine)

Sagot :

LammettHash

The identity in question is

cos(a - b) = cos(a) cos(b) + sin(a) sin(b)

so that

cos(a - b) = 12/37 cos(a) + 3/5 sin(b)

Since both a and b lie in the first quadrant, both cos(a) and sin(b) will be positive. Then it follows from the Pythagorean identity,

cos²(x) + sin²(x) = 1,

that

cos(a) = √(1 - sin²(a)) = 4/5

and

sin(b) = √(1 - cos²(b)) = 35/37

So,

cos(a - b) = 12/37 • 4/5 + 3/5 • 35/37 = 153/185

Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.