Help with a pre-calc question?

You memorize the basic facts for 30° (π/6), 45° (π/4), 60° (π/3), and 90° (π/2).

From geometry, the sides of a 30-60-90 triangle are in the ratio 1:√3:2,

and for a 45-45-90 triangle, the ratio is 1:1:√2

So for 30°, sin is ½, cos is ½√3, and tan is √3 / 3

For 60°, sin is ½√3, cos is ½, and tan is √3

For 45°, sin and cos are both ½√2, and tan is 1.

Using those as reference angles and taking the quadrant into account to get the signs right, you should know or be able to figure out very quickly all 6 trig functions for 16 different angles.

4SIN(theta) + 7 = 9 subtract 7 from both sides

4SIN(theta) = 2 divide both sides by 4

SIN(theta) = 2/4 = 1/2

now you have to use the inverse sine function: the arcsin function, which tells you the angle whose sine is 1/2. You can use sine tables or use a calculator, to find the answers: pi/6 and 5pi/6 radians.