Worksheet: Inverse Trigonometric Functions

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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 − √ 3 2 − 1 2 0 1 2 √ 2 2
𝑓 ( 𝑥 ) − 𝜋 3 − 𝜋 6 0 𝜋 4 𝜋 3
𝑥 − √ 3 2 − √ 2 2 0 √ 3 2 1
𝑔 ( 𝑥 ) − 𝜋 6 − 𝜋 4 0 𝜋 6 𝜋 2
𝑥 − 1 − 1 2 0 √ 2 2 √ 3 2
ℎ ( 𝑥 ) − 𝜋 2 − 𝜋 6 0 𝜋 4 𝜋 3
  • A ℎ ( 𝑥 )
  • B 𝑔 ( 𝑥 )
  • C 𝑓 ( 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 − 1 0 1 √ 3 1
𝑓 ( 𝑥 ) − 𝜋 3 − 𝜋 4 0 𝜋 6 𝜋 4
𝑥 − √ 3 − 1 2 0 √ 3 1
𝑔 ( 𝑥 ) − 𝜋 6 − 𝜋 4 0 𝜋 6 𝜋 2
𝑥 − 1 − 1 2 0 1 √ 3 √ 3
ℎ ( 𝑥 ) − 𝜋 4 − 𝜋 6 0 𝜋 6 𝜋 3
  • A ℎ ( 𝑥 )
  • B 𝑓 ( 𝑥 )
  • C 𝑔 ( 𝑥 )

Q3:

Find the exact value of cossin513.

  • A 1 2 1 3
  • B 1 3 1 2
  • C 5 1 3
  • D 1 3 5
  • E 5 1 2

Q4:

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

  • A1
  • B 𝜋 2
  • C 𝜋 4
  • D 𝜋 3
  • 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

𝑥 0 𝜋 6 𝜋 4 𝜋 3 𝜋 2 2 𝜋 3 3 𝜋 4 5 𝜋 6 𝜋
s i n 𝑥 0 1 2 √ 2 2 √ 3 2 1 √ 3 2 √ 2 2 1 2 0

Table B

𝑥 − 𝜋 2 − 𝜋 3 − 𝜋 4 − 𝜋 6 0 𝜋 6 𝜋 4 𝜋 3 𝜋 2
s i n 𝑥 − 1 − √ 3 2 − √ 2 2 − 1 2 0 1 2 √ 2 2 √ 3 2 1
  • 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

𝑥 0 𝜋 6 𝜋 4 𝜋 3 𝜋 2 2 𝜋 3 3 𝜋 4 5 𝜋 6 𝜋
c o s 𝑥 1 √ 3 2 √ 2 2 1 2 0 − 1 2 − √ 2 2 − √ 3 2 − 1

Table B

𝑥 − 𝜋 2 − 𝜋 3 − 𝜋 4 − 𝜋 6 0 𝜋 6 𝜋 4 𝜋 3 𝜋 2
c o s 𝑥 0 1 2 √ 2 2 √ 3 2 1 √ 3 2 √ 2 2 1 2 0
  • ATable B
  • BTable A

Q8:

Find the exact value of sinsin4𝜋3 in radians.

  • A 𝜋 3
  • B − 𝜋 3
  • C − 4 𝜋 3
  • D − 5 𝜋 3
  • E 𝜋

Q9:

Find the exact value of coscos𝜋7 in radians.

  • A 8 𝜋 7
  • B − 8 𝜋 7
  • C 6 𝜋 7
  • D 𝜋 7
  • E 𝜋

Q10:

Find the exact value of cotcot4𝜋3 in radians.

  • A − 𝜋 3
  • B 𝜋 3
  • C 𝜋
  • D − 4 𝜋 3

Q11:

Find the exact value of cossin−45.

  • A 5 4
  • B 3 5
  • C 4 5
  • D 5 2
  • E 3 4

Q12:

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

  • A 2 7 0 ∘
  • B 9 0 ∘
  • C 0 ∘
  • D 1 8 0 ∘
  • E 4 5 ∘

Q13:

Find the exact value of sinsin−5𝜋6 in radians.

  • A 𝜋
  • B 5 𝜋 6
  • C − 𝜋 6
  • D 𝜋 6

Q14:

Find the exact value of tancot35+35 in radians.

  • A 𝜋 3
  • B 𝜋
  • C 𝜋 6
  • D 𝜋 2
  • E 𝜋 4

Q15:

Find the exact value of sincos513+513 in radians.

  • A 𝜋 3
  • B 𝜋
  • C 𝜋 2
  • D 𝜋 4
  • E 𝜋 6

Q16:

Find the exact value of coscos−𝜋10 in radians.

  • A 𝜋 1 0
  • B − 9 𝜋 1 0
  • C 1 0 𝜋 1 1
  • D 9 𝜋 1 0
  • E 𝜋

Q17:

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

  • A 3 3 2 2 ′ ∘
  • B 1 0 3 2 7 ′ ∘
  • C 6 0 1 7 ′ ∘
  • D 1 4 6 3 8 ′ ∘

Q18:

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

  • A − 4 𝜋 3
  • B − 𝜋 3
  • C 2 𝜋 3
  • D 𝜋 3
  • E 𝜋

Q19:

Find the exact value of sinsin𝜋3 in radians.

  • A 𝜋
  • B 𝜋 3
  • C − 𝜋 3
  • D 4 𝜋 3
  • E 𝜋 6

Q20:

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

  • A 3 𝜋 2
  • B − 𝜋 4
  • C 𝜋 4
  • D − 𝜋 2
  • E 𝜋 2

Q21:

Find the exact value of sinsin35+45 in radians.

  • A 𝜋 6
  • B 𝜋 4
  • C 𝜋 3
  • D 𝜋
  • E 𝜋 2

Q22:

Find the exact value of csccsc−𝜋9 in radians.

  • A − 1 0 𝜋 9
  • B 8 𝜋 9
  • C 𝜋 9
  • D − 𝜋 9
  • E − 1 7 𝜋 9

Q23:

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

  • A 𝜋
  • B 2 𝜋
  • C 𝜋 4
  • D0
  • E 𝜋 3

Q24:

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

Q25:

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

  • A − 𝜋 4
  • B 𝜋 3
  • C − 𝜋 2
  • D0
  • E 𝜋 2

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