Answered

Join IDNLearn.com and start getting the answers you've been searching for. Get prompt and accurate answers to your questions from our community of experts who are always ready to help.

Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.) sin theta = 1/2 Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.) cos theta = -1

Sagot :

The solution of the given equation is :

cosθ = 1/2 when θ = π/3 + 2kπ or 5π/3 + 2kπ

cosθ = -1 when θ = π + 2kπ

Since cos2θ + sin2θ = 1, sin2θ = 1 - cos2θ

So, the given equation is equivalent to 2(1 - cos2θ) - cosθ = 1

-2cos2θ - cosθ + 1 = 0

2cos2θ + cosθ - 1 = 0 (multiplying the entire equation by -1)

(2cosθ - 1)(cosθ + 1) = 0 (taking common)

cosθ = 1/2 or cosθ = -1 (on equating it to zero)

cosθ = 1/2 when θ = π/3 + 2kπ or 5π/3 + 2kπ

cosθ = -1 when θ = π + 2kπ

For more information about trigonometric ratios, visit

https://brainly.com/question/24496175

Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. IDNLearn.com is committed to providing accurate answers. Thanks for stopping by, and see you next time for more solutions.