100% Trigonometry Double Angle Identities Assignment

If sin(x) = -1/3 and cos(x) > 0, what is tan(2x)?

-4 sqrt2/7

If cos(x) = -1/4 and tan(x) < 0, what is sin(2x)?

-sqrt 15/8

What is the value of 2cos^2 (105⁰) − 1?

-sqrt 3/2

Over the interval [0, 2π), what are the solutions to cos(2x) = cos(x)? Check all that apply.

0, 2pi/3, 4pi/3

Over the interval [0, 2π), what are the solutions to sin(2x) = sin(x)? Check all that apply.

0, pi/3, pi, 5pi/3

Write the given expression as a single trigonometric function. 2sin(2pi/8) cos(3pi/8)

sin(3pi/4)

If cos(x) = 3/4 and tan(x) < 0, what is cos(2x)?

1/8

The table shows the derivation of cos(2x). Select the correct reason for each step. Reason 1 is ___. Reason 2 is ___. Reason 3 is ___.

Addition Cosine Sum Identity Simplify

The table shows the derivation of tan(2x). Select the correct reason for each step. Reason 1 is ___. Reason 2 is ___. Readon 3 is ___.

Addition Tangent Sum Identity Simplify

The following steps show how the right side of 1 - cos(2x) = tan(x)sin(2x) can be rewritten to show it is an identity. tan(x)sin(2x) = tan(x)∙[2sin(x)cos(x)] =sin(x)/cos(x) * 2sin(x) cos(x) = 2sin2(x) = 1 - cos(2x) What are the correct justifications, listed in proper order?

Double Angle Identity, Quotient Identity for Tangent, Simplify, Double Angle Identity