find 0 for 0 < 0 < 360 sin 0 = -0.8598

Question

the question is find 0 for 0 degrees less than or equal to 0 less than 360 degrees using sin 0 = -0.8598

Answer 1

Your calculator will give you back a single angle between -90^° (Quadrant 4) and 90° (Quadrant 1) if you use the sin^-1() key.

 

 

sin(θ) will be negative in quadrants 3 and 4, so you will need to determine two angles.

 

 

sin^-1(-0.8598) = -59.3º   This the the Quadrant 4 angle.  Add 360º to get it between 0 and 360°: 360 + (-59.3) = 300.7º.

 

 

To find the Quadrant 3 angle, subtract this angle from 180º:  180 - (-59.3) = 239.3º.

 

 

It would be handy to have a unit circle or a circular protractor to see these relationships.