Algebra &Trigonometry
Sullivan & Sullivan, Fourth Edition
§ 7.1
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The Inverse Functions of Sine, Cosine
Inverse sine / cosine
Be able to evaluate the inverse of sine, cosine by hand, without a calculator
1) Evaluate sin1 (1) without using the calculator
1
2) Evaluate sin1   without using the calculator
2

3
3) Evaluate sin1    without using the calculator
 2 
4) Evaluate cos 1 (1) without using the calculator
1
 
5) cos 1   without using the calculator
2

6) cos 1  

3
 without using the calculator
2 
Inverse sine / cosine
Be able to evaluate the inverse of sine, cosine using a calculator
7) Evaluate sin1 (0.8) using the calculator, round to three decimals. Make sure that you can get the
answer both in radians, and degrees, from your calculator.
3


8) Evaluate sin1    using the calculator, round to three decimals. Make sure that you can get
 4
the answer both in radians, and degrees, from your calculator.
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Algebra &Trigonometry
Sullivan & Sullivan, Fourth Edition
§ 7.1
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9) Evaluate cos 1 (0.75) using the calculator, round to three decimals. Make sure that you can get
the answer both in radians, and degrees, from your calculator.
4
10) Evaluate cos 1    using the calculator, round to three decimals. Make sure that you can get
 7
the answer both in radians, and degrees, from your calculator.
11) Evaluate sin 1  1.5 using the calculator. What result/message do you get, and why?
12) Evaluate cos 1  1.5 using the calculator. What result/message do you get, and why?
13) What are the restrictions on the domain of y  cos 1 (x ) ?
On the domain of y  sin1 (x ) ?
Inverse of Tangent
14) What are the restrictions on the domain of y  tan1 (x ) ?
15) Evaluate tan1 (1) , without using the calculator
16) Evaluate tan1  3  , without using the calculator
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Algebra &Trigonometry
Sullivan & Sullivan, Fourth Edition
§ 7.1
17) Evaluate tan1 (1) , without using the calculator
18) Evaluate tan1 (500) using a calculator, round to three decimals.
19) Evaluate tan1  0.005  using a calculator, round to three decimals.
Composite Functions
Be able to evaluate the inverse of sine, cosine using a calculator

 

 
20) Evaluate sin1 sin    without using a calculator
6

 1 
21) Evaluate cos cos 1    without using a calculator
8

 
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Algebra &Trigonometry
Sullivan & Sullivan, Fourth Edition

 

 
§ 7.1
22) Evaluate cos 1 sin    , without using a calculator
4

 3 
  ,
 2  
23) Evaluate tan cos 1 


without using a calculator
 without using a calculator
24) Evaluate
tan cos 1 2
25) Evaluate
cos 1 tan 2 , using a calculator
,
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