sin(x)=-0.7 In degrees. How do I know which angles to solve for in -180<x<180 and which identity -180-x or 180-x for the second angle. Thanks

Answer 1

Or, if your solution is supposed to be between -180 and 180 degrees, you get -44.427 and -135.573 degrees.

How do you know which 'identity' to use? Draw a picture. Always draw a picture. Especially pictures of the unit circle. Practice until you can draw it quickly and reasonably accurately. If you have a negative sin, you know you're in Quadrants III and IV just by looking at your drawing.

Answer 2

Remember : "Add Sugar to Coffee" or "All Students take Calculus"

So in quadrant #1, ALL of the trig functions are positive

In quadrant #2, the sine function is positive

in quadrant #3, the tangent function is positive

IN quadrant #4, the cosine function is positive

sin is negative in quadrants 3 and 4.

The base angle is T = inverse_sine(0.7) = 44.427+ degrees

IN quadrant 3, that is 224.427.... degrees and in quadrant 4

that is 315.573... degrees