Pre calculus HW

Question

Simplify the expression by using a Double-Angle Formula or a Half-Angle Formula.

square root 1-cos(8theta)/2

Answer 1

sqr(1-(cos8T)/2)

half angle formula is

sin(T/2) =+/-sqr((1-cosT)/2)

for 8T

sin8T/2 = +/-sqr((1-cos8T)/2)

sine 4Theta = the simplest way to write the expression

sin4T is the answer

Answer 2

Because of the square root and that under the radical, we have a 1 - cosine, we will be using the identity:

sin(theta/2)=sqrt( (1 - cosine (theta)) / 2)

Now all we have to do is plug in the 8*theta where appropriate on the left side of the equation and simplify:

sin ((8*theta) / 2) = sin (4*theta)