Worksheet: Inverse Trigonometric Functions

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:

Find the exact value of cossin513.

  • A1213
  • B1312
  • C513
  • D135
  • E512

Q4:

Find the exact value of tan(1), in radians in terms of 𝜋, which is located in the 1st quadrant.

  • A1
  • B𝜋2
  • C𝜋4
  • D𝜋3
  • E0

Q5:

Find the exact value of tan(0) in radians.

Q6:

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

Q7:

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

Q8:

Find the exact value of sinsin4𝜋3 in radians.

  • A𝜋3
  • B𝜋3
  • C4𝜋3
  • D5𝜋3
  • E𝜋

Q9:

Find the exact value of coscos𝜋7 in radians.

  • A8𝜋7
  • B8𝜋7
  • C6𝜋7
  • D𝜋7
  • E𝜋

Q10:

Find the exact value of cotcot4𝜋3 in radians.

  • A𝜋3
  • B𝜋3
  • C𝜋
  • D4𝜋3

Q11:

Find the exact value of cossin45.

  • A54
  • B35
  • C45
  • D52
  • E34

Q12:

Which of the following is closest to arctan(10,000)?

  • A270
  • B90
  • C0
  • D180
  • E45

Q13:

Find the exact value of sinsin5𝜋6 in radians.

  • A𝜋
  • B5𝜋6
  • C𝜋6
  • D𝜋6

Q14:

Find the exact value of tancot35+35 in radians.

  • A𝜋3
  • B𝜋
  • C𝜋6
  • D𝜋2
  • E𝜋4

Q15:

Find the exact value of sincos513+513 in radians.

  • A𝜋3
  • B𝜋
  • C𝜋2
  • D𝜋4
  • E𝜋6

Q16:

Find the exact value of coscos𝜋10 in radians.

  • A𝜋10
  • B9𝜋10
  • C10𝜋11
  • D9𝜋10
  • E𝜋

Q17:

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

Q18:

Find the exact value of tantan4𝜋3, in radians in terms of 𝜋, which is located in the 1st quadrant.

  • A4𝜋3
  • B𝜋3
  • C2𝜋3
  • D𝜋3
  • E𝜋

Q19:

Find the exact value of sinsin𝜋3 in radians.

  • A𝜋
  • B𝜋3
  • C𝜋3
  • D4𝜋3
  • E𝜋6

Q20:

Find the exact value of sin(1) in radians.

  • A3𝜋2
  • B𝜋4
  • C𝜋4
  • D𝜋2
  • E𝜋2

Q21:

Find the exact value of sinsin35+45 in radians.

  • A𝜋6
  • B𝜋4
  • C𝜋3
  • D𝜋
  • E𝜋2

Q22:

Find the exact value of csccsc𝜋9 in radians.

  • A10𝜋9
  • B8𝜋9
  • C𝜋9
  • D𝜋9
  • E17𝜋9

Q23:

Find the exact value of cos(1) in radians.

  • A𝜋
  • B2𝜋
  • C𝜋4
  • D0
  • E𝜋3

Q24:

Find the exact value of sin(0) in radians.

Q25:

Find the exact value of sin(1) in radians.

  • A𝜋4
  • B𝜋3
  • C𝜋2
  • D0
  • E𝜋2

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