SOLUTION: Find all solutions to the equation below in the interval [0,2pi) Give all answers as decimals rounded to 3 places. -2sin^2(a)-cos(a)=-1

Question 1148433: Find all solutions to the equation below in the interval [0,2pi)
Give all answers as decimals rounded to 3 places.
-2sin^2(a)-cos(a)=-1

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

A couple of basics for solving trigonometric equations....

(1) Unless you have a LOT of experience, replace csc(x) with 1/sin(x), sec(x) with 1/cos(x), and cot(x) with 1/tan(x). You might further choose to replace tan(x) with sin(x)/cos(x).

(2) If the equation involves sin(x) and cos^2(x), replace the cos^2(x) with 1-sin^2(x) to get the equation in terms of sin(x) only; similarly if it involves cos(x) and sin^2(x), replace the sin^2(x) with 1-cos^2(x) to get the equation in terms of cos(x) only.

In this example, (1) is not applicable; (2) is the key. The resulting quadratic factors nicely, making it easy to find the solution set.

If you need more help with this, re-post the question, SHOWING THE WORK you have tried to do.
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