find the values between 0 and 2pi radians for which sin theta is equal to square root of three over two

Question

a trig question

Answer 1

Hi Raven,

 

It will be 60 and 120.  You can take sin^-1 of (square root 3 over 2) and that will give you 60.  This 60 is "positive angle: counter-clockwise revolution" from "positive x-axis" and also there is a 120 or -60 by measuring "negative angle: clockwise revolution" from negative x-axis (from pi or 180): 180 - 60 = 120.

 

Since sine theta is dealing with only y-values (y/r), x is neglected (ignored).  In another words, sine will be "positive" when the angles are in Q1 or Q2 (between 0 and 180) (above x-axis).

 

Here is the chart:

 

 

All angles in Unit circle are measured from x-axis.

 

 

Answer 2

Search for a diagram of a unit circle which also shows special angles.

 

http://etc.usf.edu/clipart/43200/43215/unit-circle7_43215.htm