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find all solutions of the equation in the interval [0, 2π ).

0 votes
find all solutions of the equation in the interval [0, 2π ). Use a graphing utility to graph the equation and verify the solution.

sin x/2 + cos x = 0
asked Jan 22, 2015 in TRIGONOMETRY by anonymous

1 Answer

0 votes

Step 1:

The trigonometric equation

Apply the formula

and

and

and

General solution of then .

Step 2:

Case 1:

Solve the equation  .

and

For

For

For

Step 3:

Case 2:

Solve the equation  .

image

Sine is negative in third and fourth quadrants.

image

image

image

image

The solutions are image.

The solution in the interval image is image.

Step 4:

Graph

Solution:

The solution in the interval image is image.

answered Jan 23, 2015 by david Expert
edited Jan 23, 2015 by david

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