7.8 Solving Trigonometric Equations

Definition: A trigonometric equation is an equation that contains one or more trigonometric functions.

Examples: tan(x)=sin(x)/cos(x) or 2cos(x)-1=0

From the definition given, what is the difference between a trigonometric equation and a trigonometric identity?

A trigonometric identity is true for all values of the variable. Not all trigonometric equations are true for all values.

Thus, the equation 2cos(x)-1=0 is not an identity.

But, we can solve the equation in order to find the values of x for which the equation is true.

Examples

Solve for all values of x. Write in exact form unless otherwise stated.

1) 2cos(x)-1=0 on the interval 0 < x < 360

2) cos(x)-(1/2)=0 on the interval 0 < x < 360

3) sin(x)^2+sin(x)-2=0 on the interval 0 < x < 2pi

4) 2sin(x) = (1/sin(x)) + 1 on the interval 0 < x < 360

5) 6cos(x)^2-sin(x)-5=0 on the interval 0 < x < 360 (Find approximate solutions to the nearest tenth)

Homework p. 408 #1-6 a),c),e),g)...