SOLUTION: Find all (theta) in the interval [0,2pi] satisfying a) 2sin^2(theta) + sin(theta) = 1 b) 5cos)theta) + 2cos(theta + pi) + 3sin(pi/2 - (theta)) = 3 Please show work.

Algebra ->  Trigonometry-basics -> SOLUTION: Find all (theta) in the interval [0,2pi] satisfying a) 2sin^2(theta) + sin(theta) = 1 b) 5cos)theta) + 2cos(theta + pi) + 3sin(pi/2 - (theta)) = 3 Please show work.      Log On


   

Question 743932: Find all (theta) in the interval [0,2pi] satisfying
a) 2sin^2(theta) + sin(theta) = 1
b) 5cos)theta) + 2cos(theta + pi) + 3sin(pi/2 - (theta)) = 3
Please show work.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find all (theta) in the interval [0,2pi] satisfying
a) 2sin^2(theta) + sin(theta) = 1
2sin%5E2%28x%29%2Bsin%28x%29=1
2sin%5E2%28x%29%2Bsin%28x%29-1=0
%282sin%28x%29-1%29%28sin%28x%29%2B1%29=0
2sin(x)-1=0
sin(x)=1/2
x=π/6, 5π/6
or
sin(x)+1=0
sin(x)=-1
x=3π/2
..
b) 5cos)theta) + 2cos(theta + pi) + 3sin(pi/2 - (theta)) = 3
5cos%28x%29%2B2cos%28x%2Bpi%29%2B3sin%28pi%2F2-x%29=3
5cos%28x%29-2cos%28x%29%2B3cos%28x%29=3
6cos(x)=3
cos(x)=3/6=1/2
x=π/3, 5π/3