Trigonometric Identities and Applications Quiz

Test your knowledge of trigonometric identities, functions, and applications with this comprehensive quiz. Dive into sine, cosine, tangent, and more.

Practice Learn Test

Which of the following is an identity for sine and cosine functions?

sin^2θ + cos^2θ = 1

sin(2θ) = 2sinθcosθ

sin(π/2 - θ) = cosθ

sin(-θ) = -sinθ

What is the period of the tangent function?

2π

π/2

π/4

What is the value of sin(π/3)?

1/2

√3/2

2/√3

What is the cofunction identity for secant?

sec(θ) = 1/cos(θ)

sec(θ) = 1/sin(θ)

sec(θ) = cos(θ)/sin(θ)

sec(θ) = sin(θ)/cos(θ)

Which of the following is the Pythagorean identity?

sin^2θ + cos^2θ = 1

sin(2θ) = 2sinθcosθ

sin(π/2 - θ) = cosθ

sin(-θ) = -sinθ

If sinθ = -3/5 and θ is in Quadrant III, what is the value of cosθ?

4/5

-4/5

-3/5

3/5

What is the product of secθ and cscθ?

tanθ

cotθ

sinθ

Which of the following is the double angle identity for cosine?

cos(2θ) = cos^2θ - sin^2θ

cos(2θ) = 2cos^2θ - 1

cos(2θ) = 1 - 2sin^2θ

cos(2θ) = 2sinθcosθ

What is the general solution of sin(x) = 0?

x = π/2 + nπ, where n is an integer

x = nπ, where n is an integer

x = πn, where n is an integer

x = 2nπ, where n is an integer

#10

What is the range of the secant function?

All real numbers

(-∞, -1] ∪ [1, ∞)

(-1, 1)

(-∞, 0] ∪ [0, ∞)

#11

If cos(θ) = -1/2 and θ is in Quadrant II, what is the value of tan(θ/2)?

√3/2

-√3/2

1/√3

-1/√3

#12

What is the amplitude of the function y = 2sin(3θ)?

1/2

#13

What is the derivative of sec(x)?

tan(x)

sec(x)tan(x)

csc(x)sec(x)

-csc(x)cot(x)

#14

What is the phase shift of the function y = 2sin(3θ - π/4)?

π/4

-π/4

3π/4

-3π/4

#15

What is the derivative of cot(x)?

-csc^2(x)