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Use inverse functions where needed to find all solutions of the equation in the interval (0,2pi)

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Use inverse functions where needed to find all solutions of the equation in the interval (0,2pi)

asked Jan 21, 2015 in TRIGONOMETRY by anonymous

1 Answer

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Step 1 :

The trigonometric equation is image and the interval is image.

Factorize the trigonometric equation.

image

Since the range of the inverse tangent function is image, obtain two solutions in the interval image.

Step 2 :

image

The general solution of image is image, where image is an integer.

The general solutions are image, where image is an integer.

Step 3 :

If image, then

image,

If image, then

image,

If image, then

image

The solutions are image, image, and image in the interval image.

Solution :

The solutions are image, image, and image in the interval image.

answered Jan 21, 2015 by lilly Expert

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