Answered

Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Connect with a community of experts ready to help you find solutions to your questions quickly and accurately. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

If a and b are two angles in standard position in Quadrant I, find cos(a+b) for the given function values. sin a=8/17and cos b=12/13

1) -220/221

2) -140/221

3) 140/221

4) 220/221

Sagot :

LammettHash

Recall the sum identity for cosine:

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

so that

cos(a + b) = 12/13 cos(a) - 8/17 sin(b)

Since both a and b terminate in the first quadrant, we know that both cos(a) and sin(b) are positive. Then using the Pythagorean identity,

cos²(a) + sin²(a) = 1   ⇒   cos(a) = √(1 - sin²(a)) = 15/17

cos²(b) + sin²(b) = 1   ⇒   sin(b) = √(1 - cos²(b)) = 5/13

Then

cos(a + b) = 12/13 • 15/17 - 8/17 • 5/13 = 140/221

Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.