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.


Evaluate the expression arcsinο€Ώβˆš32.

  • Aπœ‹4
  • Bπœ‹3
  • Cπœ‹2
  • Dπœ‹
  • Eπœ‹6


Evaluate the expression arccos(1).

  • A0
  • Bπœ‹6
  • Cπœ‹3
  • Dπœ‹2
  • Eπœ‹4


Evaluate the expression arctan(βˆ’1).

  • Aβˆ’πœ‹3
  • Bβˆ’πœ‹2
  • Cβˆ’πœ‹
  • Dβˆ’πœ‹4
  • Eβˆ’πœ‹6


Evaluate the expression arcsinarccosο€Ώβˆš32+ο€Ώβˆš32.

  • Aπœ‹
  • B2πœ‹3
  • Cπœ‹6
  • Dπœ‹2
  • Eπœ‹3


Evaluate the expression arctanarcsin(1)βˆ’(βˆ’1).

  • Aβˆ’3πœ‹4
  • Bβˆ’πœ‹4
  • C3πœ‹4
  • Dπœ‹4
  • E0


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

  • Aβˆ’12
  • B1
  • C12
  • Dβˆ’1
  • E0


Find the exact value of secarccosο€Όο€Όβˆ’12 without using a calculator.

  • Aβˆ’2
  • B2
  • C0
  • Dβˆ’12
  • E12


Find the exact value of arccossinο€»βˆš2ο€»βˆ’πœ‹6 without using a calculator.

  • Aβˆ’πœ‹6
  • B2πœ‹3
  • C3πœ‹4
  • Dπœ‹4
  • Eβˆ’3πœ‹4


Let arccos(π‘₯)=πœƒ, where 0<π‘₯<1 and πœƒ is in radians. Find the first two positive values of 𝛼, in terms of πœƒ, such that cos(𝛼)=π‘₯.

  • A𝛼=πœƒ, 2πœ‹βˆ’πœƒ
  • B𝛼=πœƒ, πœ‹βˆ’πœƒ
  • C𝛼=2πœƒ, 2πœ‹βˆ’πœƒ
  • D𝛼=πœƒ, πœ‹+πœƒ
  • E𝛼=πœƒ, 2πœ‹+πœƒ


Given that arccos(π‘₯)=πœƒ, where βˆ’πœ‹2<πœƒ<πœ‹2, find sin(πœƒ) in terms of π‘₯.

  • A+√1+π‘₯, βˆ’βˆš1+π‘₯
  • B√1βˆ’π‘₯
  • Cβˆ’βˆš1βˆ’π‘₯
  • D+√1βˆ’π‘₯, βˆ’βˆš1βˆ’π‘₯
  • E√1+π‘₯

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