How do you solve cos((3theta)/5 + 11)=sin ((7theta)/10 + 40s)?

1 Answer
May 17, 2017

s=((13theta)/10-101)/-40

Explanation:

Use the cofunction rule:

cos(x)=sin(90-x)
sin(x)=cos(90-x).

It doesn't really matter which one you want to convert. I will convert cos to sin. Set x equal to (3theta)/5+11

cos((3theta)/5+11)=sin(90-(3theta)/5+11)

So now we have:
sin(90-(3theta)/5+11)=sin((7theta)/10+40s)

Now, inverse sin both sides. This will cancel out the sin:

90-(3theta)/5+11=(7theta)/10+40s

Simplify so that our problem looks a little nicer:

101-(3theta)/5=(7theta)/10+40s

Move (3theta)/5 and 40s over to the other side:

101-40s=(13theta)/10

Solve for s:

-40s=(13theta)/10-101

s=((13theta)/10-101)/-40