1. Find the exact value of y, or state that y is undefined. Y=sin -1 (1) Simplify your answer. Type an exact
answer, using pi as needed. Use integers or fractions for any numbers in the expression.
Y=sin -1 (1) =

2
2. Find the exact value of y or state that y is undefined. Y=cos -1 (-square root 3 over 2) Simplify your
answer. Type an exact answer, using pi as needed. Use integers or fractions for any numbers in the
expression.



Y=cos -1 (-square root 3 over 2)  cos 1  
3  5

2  6
3. Find the exact value of y or state that y is undefined. Y = tan -1 square root3 over 3 ) Simplify your
answer. Type an exact answer, using pi as needed. Use integers or fractions for any numbers in the
expression.
 3

1 1

tan


 3 
3 6


Y = tan -1 square root3 over 3 )  tan 1 
4. Find the exact value in radians, of y or state that y is undefined. Y=cot -1 (-1) simplify answer. Type an
exact answer using pi as needed. Use integers or fractions for any numbers in the expression.
Y=cot -1 (-1)  cot y  1 
1
3
 1  tan y  1  y  tan 1  1 
tan y
4
5. Find the exact value in radians or y or state that y is undefined. Y=sec -1 (2) Type an exact answer
using pi as needed. Use integers or fractions for any numbers in the expression.
Y=sec -1 (2)  sec y  2 
1
1
1 
 2  cos y   y  cos 1 
cos y
2
2 3
6. Find the exact value of y or state that y is undefined. Y = csc -1 2 simplify answer. Type an exact
answer using pi as needed. Use integers or fractions for any numbers in the expression. Type your
answer in radians.
Y = csc -1 2  cos ec y  2 
1
1
1 
 2  sin y   y  sin 1 
sin y
2
2 6
7. Find the exact value of y or state that y is undefined. Y=cos (cos -1 (-0.3)) simplify answer, including
any radicals. Use integers or fractions for any number in the expression.
Y=cos (cos -1 (-0.3)) = - 0.3
8. Find the exact value of y or state that y is undefined. Y = tan (tan -1 8) simplify answer. Type an exact
answer using pi as needed. Use integers or fractions for any numbers in the expression. Type your
answer in radians.
Y = tan (tan -1 8) = 8
9. Find the exact value of y or state that y is undefined. Y=tan -1 ( tan 9pi/10) simplify answer. Type an
exact answer using pi as needed. Use integers or fractions for any numbers in the expression. Type your
answer in radians.
Y=tan -1 ( tan 9pi/10) 
9
10
10. Use a sketch to find the exact value of y. y= cos [tan -1 11/3] simplify answer, including any radicals.
Use integers or fractions for any numbers in the expression.
y= cos [tan -1 11/3]
Let tan 1
11
11
  or tan   .
3
3
We can draw the following triangle.
In the above triangle, cos  
Hence, y  cos cos 1
3
.
130
3
3

130
130
11. Find the exact value of y or state that y is undefined. Y=sin [tan -1 (-8)] simplify answer, including any
radicals. Use integers or fractions for any numbers in the expression.
Y=sin [tan -1 (-8)]
Let tan 1  8   or tan   8
We can draw the following triangle.
In the above triangle sin   
Hence, y  sin sin 1
8
65
8
8

65
65
12. Find the exact value of the expression sin ( sin -1 4/5 + tan -1 5/12) type an exact answer in
simplified form
sin ( sin -1 4/5 + tan -1 5/12)
Let sin 1
4
4
5
5
   sin   and tan 1    tan  
5
5
12
12
We can make the following two triangles representing α and β.
Hence, sin ( sin -1 4/5 + tan -1 5/12) = sin(   )
 sin  cos   cos  sin 
4 12 3 5 63
    
5 13 5 13 65
13. Find the exact value of the expression tan[ cos -1 (12/13) + tan -1 (3/5)] type an integer or a
simplified fraction. There seems to be mistake in typing. It should be tan[ cos -1 (12/13) + tan -1 (3/4)].
tan[ cos -1 (12/13) + tan -1 (3/4)]
Let cos 1
12
12
3
3
   cos  
and tan 1    tan  
13
13
5
4
We can make the following two triangles representing α and β.
Hence, tan[ cos -1 (12/13) + tan -1 (3/4)] = tan(   ) 
tan   tan 
1  tan  tan 
5 3

56
 12 4 
5 3 33
1 
12 4
14. Use a calculator to find the value of y in radians rounded to two decimal places. Y = cos -1 (-0.28)
type your answer in radians. Round 2 decimal places as needed.
Y = cos -1 (-0.28)  106.260  1.85 radians
15. Evualate the following expression in terms of x. sin (tan -1 6x) type an exact answer, using radicals as
needed.
sin (tan -1 6x) = sinα
if tan-16x = α or tan α =6x
Hence, we can make the following triangle.
From the above triangle, sin(tan 1 6 x)  sin  
6x
36 x 2  1