Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Get immediate and reliable solutions to your questions from a community of experienced experts on our Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

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

Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.