6.2 Trigonometric Equations I

Solving by Linear Methods

Example

Solve

Solving by Factoring

**Note: Do not divide by a variable expression.

Example

Solve

Solving by Quadratic Methods

Example

Solve

Solve Using the Quadratic Formula

Example

Find all solutions of Write the solution set

Solving by Using Trig Identities

Sometimes this means solve by Squaring (**possible extraneous roots**)

Example Check Solutions!!

Solve

Solving a Trigonometric Equation

1. Decide if the equation is linear or quadratic form, so you can determine

the solution method.

2. If only one trig function is present, solve the equation for that function.

3. If more than one trig function is present, rearrange the equation so that one

side equals 0. Then try to factor and set each factor equal to 0 to solve.

4. If the equation is quadratic in form, but not factorable, use the quadratic

formula. Check that solutions are in the desired interval.

5. Try using identities to change the form of the equation. It may be helpful to

square both sides of the equation first. If this is done, check for extraneous

solutions.

Example

A basic component of music is a pure tone. The graph below models the sinusoidal pressure y = P in pounds per square foot from a pure tone at time x = t in seconds.

a) The frequency of a pure tone is often measured in hertz. One hertz is equal to one cycle per second and is abbreviate Hz. What is the frequency f in hertz of the pure tone shown in the graph?

b) The time for the tone to produce one complete cycle is called the period. Approximate the period T in seconds of the pure tone

c) An equation for the graph is . Use a calculator to estimate the first solution to the equation that make y = .002 over the interval [0, .0182]

Ans: a) 220 Hz b) .0045 sec c) .00053 sec