Lesson Worksheet: Inverse Trigonometric Functions Mathematics • 10th Grade

In this worksheet, we will practice calculating exact values of trigonometric inverses and evaluating compositions of trigonometric and inverse trigonometric functions at standard angles in radians.

Q1:

Evaluate the expression arcsin32.

  • A𝜋4
  • B𝜋3
  • C𝜋2
  • D𝜋
  • E𝜋6

Q2:

Evaluate the expression arccos(1).

  • A0
  • B𝜋6
  • C𝜋3
  • D𝜋2
  • E𝜋4

Q3:

Evaluate the expression arctan(1).

  • A𝜋3
  • B𝜋2
  • C𝜋
  • D𝜋4
  • E𝜋6

Q4:

Evaluate the expression arcsinarccos32+32.

  • A𝜋
  • B2𝜋3
  • C𝜋6
  • D𝜋2
  • E𝜋3

Q5:

Evaluate the expression arctanarcsin(1)(1).

  • A3𝜋4
  • B𝜋4
  • C3𝜋4
  • D𝜋4
  • E0

Q6:

Find the exact value of sinarccos((0)) without using a calculator.

  • A12
  • B1
  • C12
  • D1
  • E0

Q7:

Find the exact value of secarccos12 without using a calculator.

  • A2
  • B2
  • C0
  • D12
  • E12

Q8:

Find the exact value of arccossin2𝜋6 without using a calculator.

  • A𝜋6
  • B2𝜋3
  • C3𝜋4
  • D𝜋4
  • E3𝜋4

Q9:

Let arccos(𝑥)=𝜃, where 0<𝑥<1 and 𝜃 is in radians. Find the first two positive values of 𝛼, in terms of 𝜃, such that cos(𝛼)=𝑥.

  • A𝛼=𝜃, 2𝜋𝜃
  • B𝛼=𝜃, 𝜋𝜃
  • C𝛼=2𝜃, 2𝜋𝜃
  • D𝛼=𝜃, 𝜋+𝜃
  • E𝛼=𝜃, 2𝜋+𝜃

Q10:

Given that arccos(𝑥)=𝜃, where 𝜋2<𝜃<𝜋2, find sin(𝜃) in terms of 𝑥.

  • A+1+𝑥, 1+𝑥
  • B1𝑥
  • C1𝑥
  • D+1𝑥, 1𝑥
  • E1+𝑥

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