Find all solutions in the interval [0,2π)

Calculus
Tutor: None Selected Time limit: 1 Day

sin^2(theta) + cos(theta) = 1

Mar 17th, 2015

We have given 

Sin^2(theta) + cos(theta) = 1

We know that sin^2(theta) + cos^2(theta) = 1

hence we can write : sin^2(theta) =1-cos^2(theta)

substitute the value in the given expression we get

1- cos^2(theta) + cos(theta) = 1

or we can write , 

- cos^2(theta) + cos(theta)=0

Or;  cos(theta) [1-cos(theta)]=0

Hence either 

cos(theta) =0 so theta= 90° (pi/2), 270° (3 pi/2)


Or; 1- cos(theta) =0

or :  cos(theta)=1, so theta= 0° , 180° (pi)

Answer

 theta= 90° (pi/2), 270° (3 pi/2) , 0°, 180°( pi)


Mar 17th, 2015

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