Question

1. Find the exact value by using a half-angle identity. (1 point)

sin 22.5°


A) negative one half times the square root of quantity two plus square root of two.
B) one half times the square root of quantity two plus square root of two.
C) negative one half times the square root of quantity two minus square root of two.
D) one half times the square root of quantity two minus square root of two

2. Verify the identity. (1 point)

cot x minus pi divided by two. = -tan x



PLEASE HELPP

Answer 1

1. Find the exact value by using a half-angle identity.
sin 22.5°
Using the half angle formula you get:
sin2(θ)=12[1−cos(2θ)]
if θ=22.5° then 2θ=45°
so you get:
sin2(22.5°)=12[1−cos(45°)]
sin2(22.5°)=12[1−√2/2]=2−√24
and square root both sides:
sin(22.5°)=±√2−√24=±0.382
so sin(22.5°)=0.382the answer is the letter D) one half times the square root of quantity two minus square root of two

2. Verify the identity.

cot x minus pi divided by two. = -tan x Cot(x-pi/2)=-tan(x) sin(A − B) = sin A cos B − cos A sin B sin(x – pi/2) = sin x cos (pi/2) − cos x sin (pi/2)=-cosx cos(A − B) = cos A cos B − sin A sin B cos(x− pi/2) = cos x cos pi/2 − sin x sin pi/2=-sinx Cot(x-pi/2)=cos(x-pi/2)/sin(x-pi/2) = (-sinx)/(-cosx)=-tanx--------------ok