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 ℎ(𝑥). Which function corresponds to the function sin𝑥?

𝑥−√32−12012√22
𝑓(𝑥)−𝜋3−𝜋60𝜋4𝜋3
𝑥−√32−√220√321
𝑔(𝑥)−𝜋6−𝜋40𝜋6𝜋2
𝑥−1−120√22√32
ℎ(𝑥)−𝜋2−𝜋60𝜋4𝜋3
  • Aℎ(𝑥)
  • B𝑔(𝑥)
  • C𝑓(𝑥)

Q2:

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

𝑥−√3−101√31
𝑓(𝑥)−𝜋3−𝜋40𝜋6𝜋4
𝑥−√3−120√31
𝑔(𝑥)−𝜋6−𝜋40𝜋6𝜋2
𝑥−1−1201√3√3
ℎ(𝑥)−𝜋4−𝜋60𝜋6𝜋3
  • Aℎ(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
sin𝑥012√22√321√32√22120

Table B

𝑥−𝜋2−𝜋3−𝜋4−𝜋60𝜋6𝜋4𝜋3𝜋2
sin𝑥−1−√32−√22−12012√22√321
  • 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
cos𝑥1√32√22120−12−√22−√32−1

Table B

𝑥−𝜋2−𝜋3−𝜋4−𝜋60𝜋6𝜋4𝜋3𝜋2
cos𝑥012√22√321√32√22120
  • 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 ℎ(𝑥). Which function corresponds to the function cos𝑥?

𝑥−1−12012√22
𝑓(𝑥)𝜋𝜋4𝜋2𝜋3−𝜋4
𝑥−√32−√220√321
𝑔(𝑥)5𝜋63𝜋4𝜋2𝜋60
𝑥−1−120√321
ℎ(𝑥)𝜋23𝜋4𝜋𝜋30
  • A𝑓(𝑥)
  • B𝑔(𝑥)
  • Cℎ(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 0≤𝜃≤90∘∘.

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