#1
Which of the following is an identity for sine and cosine functions?
sin^2θ + cos^2θ = 1
ExplanationPythagorean identity for sine and cosine.
#2
What is the period of the tangent function?
2π
ExplanationTangent function has a period of 2π.
#3
What is the value of sin(π/3)?
√3/2
ExplanationSine of π/3 is √3/2.
#4
What is the cofunction identity for secant?
sec(θ) = 1/cos(θ)
ExplanationCofunction identity for secant.
#5
Which of the following is the Pythagorean identity?
sin^2θ + cos^2θ = 1
ExplanationPythagorean identity for sine and cosine.
#6
If sinθ = -3/5 and θ is in Quadrant III, what is the value of cosθ?
-4/5
ExplanationUsing Pythagorean identity, cosθ = -4/5.
#7
What is the product of secθ and cscθ?
1
ExplanationMultiplying secant and cosecant yields 1.
#8
Which of the following is the double angle identity for cosine?
cos(2θ) = 1 - 2sin^2θ
ExplanationDouble angle identity for cosine.
#9
What is the general solution of sin(x) = 0?
x = nπ, where n is an integer
ExplanationGeneral solution for sin(x) = 0 is x = nπ.
#10
What is the range of the secant function?
(-∞, -1] ∪ [1, ∞)
ExplanationRange of secant function.
#11
If cos(θ) = -1/2 and θ is in Quadrant II, what is the value of tan(θ/2)?
√3/2
ExplanationUsing half-angle identity, tan(θ/2) = √3/2.
#12
What is the amplitude of the function y = 2sin(3θ)?
2
ExplanationAmplitude of y = 2sin(3θ) is 2.
#13
What is the derivative of sec(x)?
sec(x)tan(x)
ExplanationDerivative of sec(x) is sec(x)tan(x).
#14
What is the phase shift of the function y = 2sin(3θ - π/4)?
-π/4
ExplanationPhase shift of y = 2sin(3θ - π/4) is -π/4.
#15
What is the derivative of cot(x)?
-csc^2(x)
ExplanationDerivative of cot(x) is -csc^2(x).