Lesson Worksheet: Inverse Trigonometric Functions Mathematics

In this worksheet, we will practice calculating exact values of trigonometric inverses and recognizing the inverse of trigonometric functions from tables.

Q1:

The given tables show some values of 𝑓(𝑥), 𝑔(𝑥), and (𝑥). Which function corresponds to the function sin𝑥?

𝑥321201222
𝑓(𝑥)𝜋3𝜋60𝜋4𝜋3
𝑥32220321
𝑔(𝑥)𝜋6𝜋40𝜋6𝜋2
𝑥11202232
(𝑥)𝜋2𝜋60𝜋4𝜋3
  • A(𝑥)
  • B𝑔(𝑥)
  • C𝑓(𝑥)

Q2:

The given tables show some values of 𝑓(𝑥), 𝑔(𝑥), and (𝑥). Which function corresponds to the function tan𝑥?

𝑥310131
𝑓(𝑥)𝜋3𝜋40𝜋6𝜋4
𝑥312031
𝑔(𝑥)𝜋6𝜋40𝜋6𝜋2
𝑥1120133
(𝑥)𝜋4𝜋60𝜋6𝜋3
  • A(𝑥)
  • B𝑓(𝑥)
  • C𝑔(𝑥)

Q3:

Which of these two value tables shows a domain of the sine function that can be used to construct its inverse function?

Table A

𝑥0𝜋6𝜋4𝜋3𝜋22𝜋33𝜋45𝜋6𝜋
sin𝑥012223213222120

Table B

𝑥𝜋2𝜋3𝜋4𝜋60𝜋6𝜋4𝜋3𝜋2
sin𝑥132221201222321
  • ATable A
  • BTable B

Q4:

Which of these two value tables shows a domain of the cosine function that can be used to construct its inverse function?

Table A

𝑥0𝜋6𝜋4𝜋3𝜋22𝜋33𝜋45𝜋6𝜋
cos𝑥132221201222321

Table B

𝑥𝜋2𝜋3𝜋4𝜋60𝜋6𝜋4𝜋3𝜋2
cos𝑥012223213222120
  • ATable B
  • BTable A

Q5:

𝐴𝐵𝐶 is a triangle where cos𝐴=0.2327 and tan𝐵=0.9381. Find the value of 𝐶 giving the answer to the nearest minute.

  • A3322
  • B10327
  • C6017
  • D14638

Q6:

The given tables show some values of 𝑓(𝑥), 𝑔(𝑥), and (𝑥). Which function corresponds to the function cos𝑥?

𝑥11201222
𝑓(𝑥)𝜋𝜋4𝜋2𝜋3𝜋4
𝑥32220321
𝑔(𝑥)5𝜋63𝜋4𝜋2𝜋60
𝑥1120321
(𝑥)𝜋23𝜋4𝜋𝜋30
  • A𝑓(𝑥)
  • B𝑔(𝑥)
  • C(𝑥)

Q7:

True or False: If 𝜃=(𝑥)cos, then 𝑥=(𝜃)cos.

  • ATrue
  • BFalse

Q8:

True or False: coscos(𝜃)=1(𝜃).

  • ATrue
  • BFalse

Q9:

Find the exact value of sinsin(2).

Q10:

Complete the following: 𝜃=32cos, where 0𝜃90.

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