Find all solutions to the equation below in the interval [ 0 ∘ , 360 ∘ ) . sin ( 2 β ) = − 0.7

Question

i have no idea how to tackle this

Answer 1

This may be a bit difficult to follow but try to stay with me.

The first thing you must do is recognize that sine is negative in both the 3rd and 4th quadrants but the calculator will only give you the 4th quadrant answer. (and usually expressed as a negative.)

With your calculator in degree mode find sin(-1) -0.7 and get 2B = -44.43 deg

This is the 4th quadrant answer which we will write as a positive 315.57 deg (360 - 44.43).

Our 3rd quadrant result will be 224.43 deg (180 + 44.43)

Since this is all 2B and we want B we now expand the range for 2B to [0,720)

So our 2Bs will be 315.57 deg and 675.57 deg as well as 224.43 deg and 584.43 deg.

Now take half of all these to get our Bs which will be 157.79 deg, 337.79 deg, 112.22 deg and 292.22 deg.

It is usually good form to put the solutions in numerical order so we will say

B = {112.22, 157.79, 292.22, 337.79} all in degrees