Answered

Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

If cos alpha = - 5/13 and tan a < 0 , then find sin 2 alpha

Sagot :

LammettHash

Recall the Pythagorean identity,

cos²(x) + sin²(x) = 1

and the definition of tangent,

tan(x) = sin(x) / cos(x)

Given that tan(α) < 0 and cos(α) = -5/13 < 0, it follows that sin(α) > 0. Then using the identity above, we find

sin(α) = √(1 - cos²(α)) = 12/13

Now recall the double angle identity for sine,

sin(2x) = 2 sin(x) cos(x)

Then

sin(2α) = 2 sin(α) cos(α) = 2 • 12/13 • (-5/13) = -360/169

Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.