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Friday, December 21, 2012

Evaluating Inverse Trigonometric Functions

Category: Trigonometry

"Published in Newark, California, USA"

Evaluate, using principal values for the inverse functions involved



Solution:

The given equation above involves with inverse trigonometric functions. Each inverse trigonometric functions represents an angle. We can get the value of the above equation without using a calculator as follows

Let 



Express the above trigonometric function in a right triangle


Photo by Math Principles in Everyday Life

From the figure above, we can find the other trigonometric functions as follows







Let 



Express the above trigonometric function in a right triangle


Picture by Math Principles in Everyday Life

From the figure above, we can find the other trigonometric functions as follows







Now, consider the given equation



Rewrite the above equation as follows





Finally, substitute the value of each trigonometric functions to the above equation as follows