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Worksheet: Inverse of Sine and Cosine

Q1:

The given tables show some values of 𝑓 ( π‘₯ ) , 𝑔 ( π‘₯ ) , and β„Ž ( π‘₯ ) . Which function corresponds to the function s i n βˆ’ 1 π‘₯ ?

π‘₯ βˆ’ √ 3 2 βˆ’ 1 2 0 1 2 √ 2 2
𝑓 ( π‘₯ ) βˆ’ πœ‹ 3 βˆ’ πœ‹ 6 0 πœ‹ 4 πœ‹ 3
π‘₯ βˆ’ √ 3 2 βˆ’ √ 2 2 0 √ 3 2 1
𝑔 ( π‘₯ ) βˆ’ πœ‹ 6 βˆ’ πœ‹ 4 0 πœ‹ 6 πœ‹ 2
π‘₯ βˆ’ 1 βˆ’ 1 2 0 √ 2 2 √ 3 2
β„Ž ( π‘₯ ) βˆ’ πœ‹ 2 βˆ’ πœ‹ 6 0 πœ‹ 4 πœ‹ 3
  • A 𝑔 ( π‘₯ )
  • B 𝑓 ( π‘₯ )
  • C β„Ž ( π‘₯ )

Q2:

The given tables show some values of 𝑓 ( π‘₯ ) , 𝑔 ( π‘₯ ) , and β„Ž ( π‘₯ ) . Which function corresponds to the function c o s βˆ’ 1 π‘₯ ?

π‘₯ βˆ’ 1 βˆ’ 1 2 0 1 2 √ 2 2
𝑓 ( π‘₯ ) πœ‹ πœ‹ 4 πœ‹ 2 πœ‹ 3 βˆ’ πœ‹ 4
π‘₯ βˆ’ √ 3 2 βˆ’ √ 2 2 0 √ 3 2 1
𝑔 ( π‘₯ ) 5 πœ‹ 6 3 πœ‹ 4 πœ‹ 2 πœ‹ 6 0
π‘₯ βˆ’ 1 βˆ’ 1 2 0 √ 3 2 1
β„Ž ( π‘₯ ) πœ‹ 2 3 πœ‹ 4 πœ‹ πœ‹ 3 0
  • A 𝑓 ( π‘₯ )
  • B β„Ž ( π‘₯ )
  • C 𝑔 ( π‘₯ )

Q3:

Find the exact value of s i n βˆ’ 1 ( 1 ) in radians.

  • A 3 πœ‹ 2
  • B βˆ’ πœ‹ 4
  • C βˆ’ πœ‹ 2
  • D πœ‹ 2
  • E πœ‹ 4

Q4:

Find the exact value of c o s βˆ’ 1 ( βˆ’ 1 ) in radians.

  • A 2 πœ‹
  • B0
  • C πœ‹ 3
  • D πœ‹
  • E πœ‹ 4

Q5:

Find the exact value of s i n βˆ’ 1 ( 0 ) in radians.

Q6:

Find the exact value of c o s βˆ’ 1 1 in radians.

Q7:

Find the exact value of s i n βˆ’ 1 ( βˆ’ 1 ) in radians.

  • A πœ‹ 3
  • B πœ‹ 2
  • C βˆ’ πœ‹ 4
  • D βˆ’ πœ‹ 2
  • E0

Q8:

Find the exact value of c o s βˆ’ 1 0 in radians.

  • A πœ‹
  • B0
  • C πœ‹ 4
  • D πœ‹ 2