Question

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

Answer 1

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  .

Sine is negative in third and fourth quadrants.

The solutions are .

The solution in the interval is .

Step 4:

Graph

Solution:

The solution in the interval is .