This is a free lesson from our course in Trigonometry
In this lesson you'll learn with the help of several examples with solution how
to evaluate expressions which involve inverse trigonometric functions and values of sin^{1}
1, cos^{1 }1/2, tan^{1 }
3, cos^{1 }
3/2, cos^{1 }
1 and sin^{1}
2/2. When you
evaluate an inverse trigonometric function you are asking what angle measure, say
, did you plug into
the trig function (remember regular, and not inverse!) to get x.
Theorems :
• y = sin^{1} x is equivalent to sin y = x with 1 < x < 1 and 
/ 2 <= y <=
/ 2
• y = cos^{1} x is equivalent to cos y = x with 1 < x < 1 and 0 <= y <=
• y = tan^{1} x is equivalent to tan y = x with 
/ 2 < y <
/ 2
(Continued from above)
E.g.: sin^{1}(
3 / 2)
Let, y = sin^{1}(
3 / 2).
According to theorem 1 above, this is equivalent to sin y = 
3 / 2 , with 
/ 2 <= y <=
/ 2
sin (
/3) =
3 / 2.
You also know that sin(x) =  sin x. So sin (
/ 3) = 
3 / 2
Comparing the last expression with the equation sin y = 
3 / 2, we conclude
that y = 
/ 3
The values of inverse functions can be written in both radians and degrees. All this will be explained to you by the instructor
with the help of video and solving problems related to inverse trigonometric functions.
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