mayy024
Answered

Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Given: cos a = -3/5, sin b = 5/13, and a and b are second-quadrant angles; find sin(a - b).

63/65
-33/65
33/65

Sagot :

Answer:

63/65

Step-by-step explanation:

Recall that sin(a-b) = sin(a)cos(b) - cos(a)sin(b)

Therefore, we have:

sin(a-b) = sin(a)cos(b) - (-3/5)(5/13)

sin(a-b) = sin(a)cos(b) + 3/13

Since sin(x) = opposite/hypotenuse and cos(x) = adjacent/hypotenuse, then if cos(a) = -3/5, sin(a) = 4/5. Likewise, if sin(b) = 5/13, then cos(b) = 12/13.

Therefore, sin(a-b) = (4/5)(12/13) + 3/13 = 48/65 + 3/13 = 48/65 + 15/65 = 63/65

Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We hope this was helpful. Please come back whenever you need more information or answers to your queries. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.