Find sin(x) given cos(2x)

Question

If cos(2x)=4/5 and x terminates in quadrant 1, then find sin(x)

Answer 1

cos(2x) = 1 - 2sin²x

 

4/5 = 1 - 2sin²x

 

-1/5 = -2sin²x

 

sin²x = 1/10

 

Since x terminates in QI, sinx > 0

 

So, sinx  = √(1/10) = √10/10

 

 

Answer 2

Will your teacher let you use a calculator?  Will your teacher let you use inverse trig functions?

 

The "easy" way is to take the inverse cosine of both sides, freeing up the argument of the cosine.

 

2x = cos^-1(4/5)

 

2x = 36.86989765

 

x = 36.86989765/2 = 18.43494882

 

Find the sin(36.86989765) = .31622