without using a calculator.Examples on Using Inverse Trigonometric Functions:
Example 1:
Find the value of without using a calculator.
Solution:
Since 
is in the range of 
, we can use the characteristic of undo the effect of each other between a trigonometric function and its inverse.
Example 2:
Find the value of 
without using a calculator.
Solution:
Since is in the domain of , we can use the characteristic of undo the effect of each other between a trigonometric function and its inverse.
Example 3:
Find the value of 
without using a calculator.
Solution:
Since 
is in the range of , we can not use the characteristic of undo the effect of each other between a trigonometric function and its inverse.
We need to solve in two steps:
(because 0 is in the domain of 
)
Example 4:
Find the value of 
without using a calculator.
Solution:
means that "what is the angle whose sine is and in the range 
.
Let 
Because 
is in the domain of
Example 5:
Find the value of 
without using a calculator.
Solution:
means that "what is the angle whose cosecant is 
and in the range except 0.
Let 
Because 
is in the domain of 
Example 6:
Solve the equation 
Solution:
Solve the equation means find the unknown x,
For this equation to be valid, 
should be in the domain of 
and since 
is in the range of , then
Example 7:
Given that 
, 
, find 
.
Solution:
Since y is in the range of 
, then
Using a right angle triangle to demonstrate this angle
From the triangle we can recognize that 