lowering powers

Question

1.  Find sin 2x, cos 2x, and tan 2x from the given information.

        3 sin x=5/13  x is in Quadrant I

 

 

2. Use the formulas for lowering powers to rewrite the expression in terms of the ?rst power of cosine

      sin^4 x

Answer 1

1)

 

First, we solve for sinx.

 

Divide both sides of the equation by 3.

 

sinx = 5 / 39

 

 

x = sin^-1(5/39)

x = 7.37

 

 

Now just plug in this value of x into the double angle expressions.

 

 

2)

 

sin⁴x = (sin²x)²

 

 

Using the identity of 1:   sin²x + cos²x = 1

 

 

(sin²x)²= (√(1 - cos²x))²

 

 

square-root and power of 2 cancel each other out.

 

1 - cos²x = (1 + cosx)(1 - cosx)