Double Angle Identities in Trigonometry

This video tutorial focuses on simplifying trigonometric identities using double angle formulas. It covers several examples, demonstrating how to transform expressions into simpler forms by recognizing and applying double angle identities. The tutorial emphasizes the importance of factoring and adjusting coefficients to match the standard double angle formulas. By the end, viewers should be able to derive, evaluate, and simplify expressions using these identities.

What is the main goal when working with double angle identities?

• To eliminate all cosine terms

• To expand expressions into multiple trig functions

• To simplify expressions to a single trig function

• To convert all expressions to sine functions

Which double angle identity is used for the expression 4 sin(θ) cos(θ)?

• cos(2θ) = 2 cos²(θ) - 1

• cos(2θ) = cos²(θ) - sin²(θ)

• tan(2θ) = 2 tan(θ) / (1 - tan²(θ))

• sin(2θ) = 2 sin(θ) cos(θ)

How do you simplify 6 sin(7θ) cos(7θ) using double angle identities?

• 3 sin(14θ)

• 6 sin(14θ)

• 3 cos(14θ)

• 6 cos(14θ)

What is the result of doubling the angle in the expression 2 sin(3θ) cos(3θ)?

• cos(6θ)

• cos(3θ)

• sin(6θ)

• sin(3θ)

Which identity is used to simplify 4 - 8 sin²(5x)?

• cos(2x) = 2 cos²(x) - 1

• tan(2x) = 2 tan(x) / (1 - tan²(x))

• sin(2x) = 2 sin(x) cos(x)

• cos(2x) = 1 - 2 sin²(x)

What is the simplified form of 4 - 8 sin²(5x) using double angle identities?

• 8 sin(10x)

• 4 cos(10x)

• 4 sin(10x)

• 8 cos(10x)

How do you simplify 2 cos²(x) - 1 using double angle identities?

• sec(2x)

• cos(2x)

• tan(2x)

• sin(2x)

What factor is used to simplify 2 cos²(x) - 1/3?

• 1/2

• 1/5

• 1/4

• 1/3

What is the final expression for 2 cos²(x) - 1/3 using double angle identities?

• 1/5 cos(2x)

• 1/2 cos(2x)

• 1/4 cos(2x)

• 1/3 cos(2x)

What is the purpose of using double angle identities in trigonometry?

• To convert all expressions to tangent functions

• To increase the complexity of expressions

• To eliminate all sine terms

• To simplify expressions to a single trigonometric function