How do I find all the solutions of 'sin^2(x) = 1-cosx' in terms of radians from zero to 2pi?

Find all solutions of the equation in the interval [0, 2pi]

1 Answer
Apr 19, 2018

0, pi/2, (3pi)/2

Explanation:

sin^2x=1-cosx

1-cos^2x=1-cosx

-cos^2x+cosx=0

cos^2x-cosx=0 Multiplying both sides by -1

cosx(cosx-1)=0 Factoring the left side

Set sides equal to zero

Cosx=0

or

Cosx-1=0
Cosx=1

Find instances where cosx is equal to '1' and '0'

Answers: 0, pi/2, (3pi)/2