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Saturday, April 27, 2013

Solving Trigonometric Equations, 4

Category: Trigonometry, Algebra

"Published in Suisun City, California, USA"

Find the value of x for 



Solution:

Consider the given equation above



By looking at the equation above, the factors of 4sin x cos x are 2sin x and 2cos x while the factors of -1 are 1 and -1. Since there are 2sin x, -2cos x, and -1 in the equation above, then we can rewrite the above equation as follows



Equate each factor to zero and solve for the value of x.

If
then







Since the value of sine is positive at 1st and 2nd Quadrant, then 





where n is the number of revolutions.

If
then







Since the value of cosine is negative at 2nd and 3rd Quadrant, then 





where n is the number of revolutions.