14.714.7

Solving Trig EquationsSolving Trig Equations

Find all solutions of for the interval0 < 360.

Original equation

Solve for 0.

Distributive Property

Divide each side by –1.

Simplify.

Factor.

Example:

Now use the Zero Product Property.

Answer: The solutions are 30°, 150°, and 270°.

or

Find all solutions of for the interval 0 < 2.

Original equation

Solve for 0.

Factor

Example:

Use the Zero Product Property.

Answer: The solutions are

or

Find all solutions of each equation for the given interval.

a.

b.

Answer:

Answer:

More problems:

Solve for all values of ifis measured in radians.

Original equation

Subtract

Factor.

or Zero Product Property

Solve.

Example:

Look at the graph of to find solutions of

The solutions are and so on, and

so on.

The only solution in the interval 0 to are and

The period of the sine function is radians. So the

solutions can be written as and

where k is any integer.

Similarly, the solutions for

Answer: The solutions are

and

Solve for all values of if ismeasured in degrees.

Original equation

Solve for 0.

Factor.

Example:

Solve for in the interval of

or

Answer: The solutions are

a. Solve for all values of if ismeasured in radians.

b. Solve for all values of if ismeasured in degrees.

Answer:

Answer:

There is more:

Solve

Original equation

Multiply.

Factor.

Example:

or

Thus, is not a solution.

is undefined.

Answer: The solution is

Check

Solve

Answer: The solution is .

Your turn:

Solve

Subtract 1 and addto each side.

Original equation

Multiply each side by 4.

Factor.

Example:

or

is undefined for

Answer: The solutions areand

Solve

Answer:

Your turn again: