Trigonometric Equations and Applications

In section 8-1 we learned how to solve for theta while using inverses. Basically , you are solving an equation with a trig function. An inverse almost always has two answers. You must also remember that your calculator must be in degree mode. If the answer is asked for in radians, wait until the end and use the formula pi/180 to convert to radians.
FIRST;
Get the trig function by itself.
2sinex +6=0
*Subtract six .
Divide both sides by two; sin therefore is equal to 3.
NEXT;
Make variable equal to the inverse of the trig function.
X= sin^-1 (3)
LASTLY;
Solve for x while using coordinate plane.

Ex. 1
Sinx=(-4)
X=sin^-1 (4)
Because sine can never be 4,or greater than 1 for the matter, the answer therefore is NO SOLUTION.

Ex.2.
Csc x= (2)
X= csc^-1 (2) * Csc is related to the sine function therefore you use the inverse of sine.
X=sin^-1 (1/2) * You must also find the reciprocal in order to make the statement true.
X=30

Sine is positive in both quadrant 1 and 2. We already know that sin^-1 is 30 in quadrant 1. In order to find sin^-1 in quadrant 2, we make the number (30) negative and add 180.

-(30)+ 180 = 150

The answer is x=30
x= 150