Trigonometric Identities and Functions

The video tutorial covers trigonometric identities, focusing on even and odd functions, reciprocal identities, and simplification techniques. It explains how to verify identities using algebraic manipulation and Pythagorean identities. The tutorial also demonstrates converting between different trigonometric functions and proving or disproving given identities. The session concludes with a final verification of identities.

What happens to an even function like cosine when it is squared?

• It becomes an odd function.

• It remains an even function.

• It becomes neither even nor odd.

• It becomes undefined.

Tags

CCSS.HSF.TF.A.2

Why is the secant function undefined at certain points?

• Because secant is always undefined.

• Because sine is zero at those points.

• Because tangent is undefined at those points.

• Because cosine is zero at those points.

How do you simplify the expression sine(x) * cosine(x) * secant(x)?

• It remains unchanged.

• It simplifies to cosine(x).

• It simplifies to sine(x).

• It simplifies to tangent(x).

What is the result of simplifying the expression (1 - cosine^2(x)) / tangent^2(x)?

• tangent^2(x)

• secant^2(x)

• cosine^2(x)

• sine^2(x)

Which identity is used to verify that cosine^2(x) + sine^2(x) equals 1?

• Quotient Identity

• Even-Odd Identity

• Pythagorean Identity

• Reciprocal Identity

Tags

CCSS.HSF.TF.C.8

How can you express secant in terms of cotangent?

• secant = cotangent^2 + 1

• secant = sqrt(1 + cotangent^2)

• secant = 1 / sine

• secant = 1 / tangent

What is the result of verifying the identity: 1 + cotangent^2(x) = cosecant^2(x)?

• True

• Undefined

• False

• Partially True

What is the simplified form of the expression: (1 - sine(x)) * (1 + sine(x))?

• 1 + sine^2(x)

• cosine^2(x)

• 1 - sine^2(x)

• sine^2(x)

How do you verify the identity: 3 + cosine^2(theta) = 3 + cosine^2(x)?

• By using the quotient identity

• By using the even-odd identity

• By using the reciprocal identity

• By using the Pythagorean identity

What is the final form of the expression: negative 4 tangent(x) times secant(x)?

• 4 secant(x)

• -4 tangent(x) secant(x)

• -4 secant(x)

• 4 tangent(x) secant(x)