Solve 11sin(theta)-2=2 for a value of theta when 0 <= theta <= pi/2.?

I think I know how to do the first one but I'm unsure about how to do the second problem enter image source here

2 Answers
Oct 26, 2017

theta = 0.659

Explanation:

5cos2theta+7=cos2theta+8

Simplifies to (simply by rearranging):
4cos2theta=1

We know theta=1.32 by using inverse cos, and now we need to find out 2theta.

2theta=1.32
theta = 0.659

Oct 26, 2017

Given: 5cos(2theta)+7=cos(2theta)+8; 0 <= theta <= pi/2

Subtract 7 from both sides:

5cos(2theta)=cos(2theta)+1; 0 <= theta <= pi/2

Subtract cos(2theta) from both sides:

4cos(2theta)=1; 0 <= theta <= pi/2

Divide both sides by 4:

cos(2theta)=1/4; 0 <= theta <= pi/2

Use the inverse cosine on both sides:

2theta= cos^-1(1/4); 0 <= theta <= pi/2

Divide both sides by 2:

theta = 1/2cos^-1(1/4); 0 <= theta <= pi/2

theta = 0.659