SOLUTION: Find all solutions to the given equation. (Enter your answers as a comma-separated list. Let k be any integer. If there is no solution enter DNE.) 2 cos^2 θ − sin &#9

Algebra ->  Trigonometry-basics -> SOLUTION: Find all solutions to the given equation. (Enter your answers as a comma-separated list. Let k be any integer. If there is no solution enter DNE.) 2 cos^2 θ − sin &#9      Log On


   

Question 924299: Find all solutions to the given equation.
(Enter your answers as a comma-separated list. Let k be any integer. If there is no solution enter DNE.)
2 cos^2 θ − sin θ = 1
θ =

Thank you
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
2cos%5E2%28theta%29+-+sin%28theta%29+=+1

Replace cos%5E2%28theta%29 by 1-sin%5E2%28theta%29

2%281%5E%22%22-sin%5E2%28theta%29%5E%22%22%29+-+sin%28theta%29+=+1

2-2sin%5E2%28theta%29+-+sin%28theta%29+=+1

2-2sin%5E2%28theta%29+-+sin%28theta%29+-+1=0

-2sin%5E2%28theta%29+-+sin%28theta%29+%2B+1=0

2sin%5E2%28theta%29+%2B+sin%28theta%29+-+1=0

%282sin%28theta%29%5E%22%22-1%29%28sin%28theta%29%5E%22%22%2B1%29=0

2sin%28theta%29-1=0; sin%28theta%29%2B1=0

sin%28theta%29=1%2F2;  sin%28theta%29=-1

For sin%28theta%29=1%2F2;

theta=pi%2F6%2B2pi%2Ak;  theta=5pi%2F6%2B2pi%2Ak


For sin%28theta%29=-1

theta=3pi%2F2%2B2pi%2Ak

Edwin