#1
Which reciprocal trigonometric function is equivalent to 1/sin(x)?
csc(x)
ExplanationCosecant function is the reciprocal of the sine function.
#2
If sec(x) = 2, what is the value of cos(x)?
0.5
ExplanationCosine is the reciprocal of secant, so cos(x) = 1/sec(x) = 1/2 = 0.5.
#3
If sin(x) = 3/5, what is the value of csc(x)?
5/3
ExplanationCosecant is the reciprocal of sine, so csc(x) = 1/sin(x) = 1/(3/5) = 5/3.
#4
What is the period of the function y = sec(2x)?
π/2
ExplanationThe period of the secant function with argument 2x is half of the regular period, which is π/2.
#5
If cos(x) = -4/5, what is the value of sec(x)?
-5/3
ExplanationSecant is the reciprocal of cosine, so sec(x) = 1/cos(x) = 1/(-4/5) = -5/4 = -5/3.
#6
What is the range of the cotangent function?
(-∞, -1) ∪ (1, ∞)
ExplanationThe cotangent function has a range of negative infinity to -1, union 1 to positive infinity.
#7
If cos(θ) = 4/5, what is the value of sec(θ)?
5/3
ExplanationSecant is the reciprocal of cosine, so sec(θ) = 1/cos(θ) = 1/(4/5) = 5/4 = 5/3.
#8
If tan(θ) = -√3, what is the value of cot(θ)?
1/√3
ExplanationCotangent is the reciprocal of tangent, so cot(θ) = 1/tan(θ) = 1/(-√3) = -1/√3.
#9
What is the derivative of the function y = csc(x) with respect to x?
-csc(x)cot(x)
ExplanationThe derivative of cosecant function is -cosecant(x) cotangent(x).
#10
If sec(θ) = -√2, what is the value of cos(θ)?
-1/√2
ExplanationCosine is the reciprocal of secant, so cos(θ) = 1/sec(θ) = 1/(-√2) = -1/√2.
#11
What is the derivative of the function y = cot(x) with respect to x?
-csc^2(x)
ExplanationThe derivative of cotangent function is -cosecant squared.
#12
What is the integral of the function y = sec(x) with respect to x?
ln|sec(x) + tan(x)| + C
ExplanationThe integral of secant function is the natural logarithm of the absolute value of (sec(x) + tan(x)), plus the constant of integration.
#13
What is the integral of the function y = cot(x) with respect to x?
ln|sin(x)| + C
ExplanationThe integral of cotangent function is the natural logarithm of the absolute value of sine(x), plus the constant of integration.
#14
What is the integral of the function y = csc(x) with respect to x?
-ln|csc(x) - cot(x)| + C
ExplanationThe integral of cosecant function is the negative natural logarithm of the absolute value of (cosecant(x) - cotangent(x)), plus the constant of integration.
#15
What is the integral of the function y = sec(x)tan(x) with respect to x?
sec(x)ln|sec(x) + tan(x)| + C
ExplanationThe integral of secant tangent product is secant times the natural logarithm of the absolute value of (sec(x) + tan(x)), plus the constant of integration.