Lesson Worksheet: Inverse Trigonometric Functions Mathematics • 10th Grade

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(π‘₯), 𝑔(π‘₯), and β„Ž(π‘₯). Which function corresponds to the function sinπ‘₯?

π‘₯βˆ’βˆš32βˆ’12012√22
𝑓(π‘₯)βˆ’πœ‹3βˆ’πœ‹60πœ‹4πœ‹3
π‘₯βˆ’βˆš32βˆ’βˆš220√321
𝑔(π‘₯)βˆ’πœ‹6βˆ’πœ‹40πœ‹6πœ‹2
π‘₯βˆ’1βˆ’120√22√32
β„Ž(π‘₯)βˆ’πœ‹2βˆ’πœ‹60πœ‹4πœ‹3
  • Aβ„Ž(π‘₯)
  • B𝑔(π‘₯)
  • C𝑓(π‘₯)

Q2:

The given tables show some values of 𝑓(π‘₯), 𝑔(π‘₯), and β„Ž(π‘₯). Which function corresponds to the function tanπ‘₯?

π‘₯βˆ’βˆš3βˆ’101√31
𝑓(π‘₯)βˆ’πœ‹3βˆ’πœ‹40πœ‹6πœ‹4
π‘₯βˆ’βˆš3βˆ’120√31
𝑔(π‘₯)βˆ’πœ‹6βˆ’πœ‹40πœ‹6πœ‹2
π‘₯βˆ’1βˆ’1201√3√3
β„Ž(π‘₯)βˆ’πœ‹4βˆ’πœ‹60πœ‹6πœ‹3
  • Aβ„Ž(π‘₯)
  • B𝑓(π‘₯)
  • C𝑔(π‘₯)

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

π‘₯0πœ‹6πœ‹4πœ‹3πœ‹22πœ‹33πœ‹45πœ‹6πœ‹
sinπ‘₯012√22√321√32√22120

Table B

π‘₯βˆ’πœ‹2βˆ’πœ‹3βˆ’πœ‹4βˆ’πœ‹60πœ‹6πœ‹4πœ‹3πœ‹2
sinπ‘₯βˆ’1βˆ’βˆš32βˆ’βˆš22βˆ’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

π‘₯0πœ‹6πœ‹4πœ‹3πœ‹22πœ‹33πœ‹45πœ‹6πœ‹
cosπ‘₯1√32√22120βˆ’12βˆ’βˆš22βˆ’βˆš32βˆ’1

Table B

π‘₯βˆ’πœ‹2βˆ’πœ‹3βˆ’πœ‹4βˆ’πœ‹60πœ‹6πœ‹4πœ‹3πœ‹2
cosπ‘₯012√22√321√32√22120
  • ATable B
  • BTable A

Q5:

𝐴𝐡𝐢 is a triangle where cos𝐴=0.2327 and tan𝐡=0.9381. Find the value of ∠𝐢 giving the answer to the nearest minute.

  • A3322β€²βˆ˜
  • B10327β€²βˆ˜
  • C6017β€²βˆ˜
  • D14638β€²βˆ˜

Q6:

The given tables show some values of 𝑓(π‘₯), 𝑔(π‘₯), and β„Ž(π‘₯). Which function corresponds to the function cosπ‘₯?

π‘₯βˆ’1βˆ’12012√22
𝑓(π‘₯)πœ‹πœ‹4πœ‹2πœ‹3βˆ’πœ‹4
π‘₯βˆ’βˆš32βˆ’βˆš220√321
𝑔(π‘₯)5πœ‹63πœ‹4πœ‹2πœ‹60
π‘₯βˆ’1βˆ’120√321
β„Ž(π‘₯)πœ‹23πœ‹4πœ‹πœ‹30
  • A𝑓(π‘₯)
  • B𝑔(π‘₯)
  • Cβ„Ž(π‘₯)

Q7:

True or False: If πœƒ=(π‘₯)cos, then π‘₯=(πœƒ)cos.

  • ATrue
  • BFalse

Q8:

True or False: coscos(πœƒ)=1(πœƒ).

  • ATrue
  • BFalse

Q9:

Find the exact value of sinsinο€Ί(2)ο†οŠ±οŠ§.

Q10:

Complete the following: πœƒ=√32cos, where 0β‰€πœƒβ‰€90∘∘.

This lesson includes 11 additional questions and 91 additional question variations for subscribers.

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