Reciprocal Trigonometric Functions and Their Applications Quiz

Test your understanding of trigonometry with these questions on reciprocal trigonometric functions, derivatives, integrals & more!

Practice Learn Test

Which reciprocal trigonometric function is equivalent to 1/sin(x)?

sec(x)

csc(x)

cot(x)

cos(x)

If sec(x) = 2, what is the value of cos(x)?

0.5

0.25

1/2

If sin(x) = 3/5, what is the value of csc(x)?

5/3

3/5

4/5

5/4

What is the period of the function y = sec(2x)?

2π

π/2

π/4

If cos(x) = -4/5, what is the value of sec(x)?

-5/4

-4/3

-5/3

-3/4

What is the range of the cotangent function?

(-∞, -1) ∪ (1, ∞)

(-1, 1)

(-π/2, π/2)

(-π, π)

If cos(θ) = 4/5, what is the value of sec(θ)?

5/4

4/3

5/3

3/4

If tan(θ) = -√3, what is the value of cot(θ)?

-1/√3

1/√3

-√3

√3

What is the derivative of the function y = csc(x) with respect to x?

-csc(x)cot(x)

csc(x)cot(x)

csc^2(x)

-csc^2(x)

#10

If sec(θ) = -√2, what is the value of cos(θ)?

-√2

1/√2

-1/√2

√2

#11

What is the derivative of the function y = cot(x) with respect to x?

-csc^2(x)

-cot(x)csc(x)

csc^2(x)

cot(x)csc(x)

#12

What is the integral of the function y = sec(x) with respect to x?

ln|sec(x) + tan(x)| + C

ln|sec(x) - tan(x)| + C

ln|sec(x) + cot(x)| + C

ln|sec(x) - cot(x)| + C

#13

What is the integral of the function y = cot(x) with respect to x?

ln|sin(x)| + C

ln|cos(x)| + C

ln|tan(x)| + C

ln|csc(x)| + C

#14

What is the integral of the function y = csc(x) with respect to x?

-ln|csc(x) + cot(x)| + C

-ln|csc(x) - cot(x)| + C

ln|csc(x) + cot(x)| + C

ln|csc(x) - cot(x)| + C

#15

What is the integral of the function y = sec(x)tan(x) with respect to x?

sec(x) + C

sec(x)ln|sec(x) + tan(x)| + C

sec(x)ln|sec(x) - tan(x)| + C

sec(x)ln|sec(x) + cot(x)| + C