Trigonometry Identities Quiz

What is the reciprocal of sine?

• Cosine

• Secant

• Cosecant

• Cotangent

How is cosine related in terms of secant?

• 1 over tangent

• 1 over cosecant

• 1 over secant

• 1 over cotangent

What is the reciprocal relationship of cotangent?

• 1 over secant

• 1 over tangent

• 1 over cosine

• 1 over sine

What is the quotient identity for tangent?

• Cosine over sine

• Sine over cosine

• Cosecant over secant

• Secant over cosecant

How can trig identities help in mathematics?

• By creating complex equations

• By defining new trig functions

• By limiting the use of algebra

• By simplifying trig expressions

Which of the following represents the Pythagorean identity?

• sin²θ + cos²θ = 1

• tan²θ + 1 = sec²θ

• sin²θ = 1 - cos²θ

• 1 + cot²θ = csc²θ

Answer explanation

The Pythagorean identity is sin²θ + cos²θ = 1, making it the correct choice among the options provided.

What is the cofunction identity for tan(θ)?

• tan(θ) = cot(π/2 - θ)

• cot(θ) = tan(π/2 - θ)

• sin(θ) = cos(π/2 - θ)

• sec(θ) = csc(π/2 - θ)

Answer explanation

The correct cofunction identity for tan(θ) is tan(θ) = cot(π/2 - θ), making the first option the right choice.

Which identity represents the even-odd property for cos(θ)?

• cos(−θ) = cos(θ)

• sin(−θ) = −sin(θ)

• tan(−θ) = −tan(θ)

• sec(−θ) = sec(θ)

Answer explanation

The even-odd property for cos(θ) is represented by cos(−θ) = cos(θ), making the correct answer choice cos(−θ) = cos(θ).

What is the double-angle identity for sin(2θ)?

• sin(2θ) = 2sin(θ)cos(θ)

• cos(2θ) = cos²θ − sin²θ

• tan(2θ) = 2tan(θ)/(1 − tan²θ)

• sin(2θ) = 1 − 2sin²θ

Answer explanation

The double-angle identity for sin(2θ) is sin(2θ) = 2sin(θ)cos(θ), which matches the correct answer choice.

Which of the following is a sum-to-product identity for sin(A + B)?

• sin(A + B) = 2sin[(A + B)/2]cos[(A − B)/2]

• cos(A + B) = 2cos[(A + B)/2]cos[(A − B)/2]

• sin(A + B) = 2cos[(A + B)/2]sin[(A − B)/2]

• cos(A + B) = 2sin[(A + B)/2]sin[(A − B)/2]

Answer explanation

The correct sum-to-product identity for sin(A + B) is sin(A + B) = 2sin[(A + B)/2]cos[(A − B)/2]