Exploring Even and Odd Trigonometric Functions

The video tutorial explains the concepts of even and odd functions, highlighting their symmetrical properties. It discusses how these properties apply to trigonometric functions, specifically cosine and sine, and introduces reflection identities. A proof is provided to demonstrate the use of these identities in solving trigonometric equations.

What is a key characteristic of an even function?

• Its graph is not symmetrical.

• Its graph is symmetrical about the origin.

• Its graph is symmetrical about the y-axis.

• Its graph is symmetrical about the x-axis.

Which of the following is true for an odd function?

• f(-x) = f(x)

• f(x) = 0

• f(x) = -f(x)

• f(-x) = -f(x)

For an even function, if f(x) = y, what is f(-x)?

• y

• 0

• -y

• x

For an odd function, if f(x) = y, what is f(-x)?

• x

• -y

• 0

• y

Why are even and odd functions discussed in trigonometry?

• Because they have no relevance in trigonometry.

• Because cosine is an even function and sine is an odd function.

• Because all trigonometric functions are odd.

• Because all trigonometric functions are even.

Which trigonometric function is even?

• Cosecant

• Sine

• Tangent

• Cosine

What is the value of cosine(-θ)?

• cos(θ)

• sin(θ)

• -sin(θ)

• -cos(θ)

What is the value of sine(-θ)?

• -sin(θ)

• -cos(θ)

• sin(θ)

• cos(θ)

In the proof, what identity is used to replace 1 - sin²(θ)?

• sin²(θ)

• cos²(θ)

• 1 - cos²(θ)

• tan²(θ)

What should you replace sine(-θ) with in a reflection identity?

• -sin(θ)

• -cos(θ)

• cos(θ)

• sin(θ)