00:01
In this video, we will find the value of theta using the equation 15 sine 2 theta squared plus sine 2 theta minus 2 equals 0.
00:11
The first thing we can do is substitute in x in place of sine of 2 theta, which gives us 15x squared plus x minus 2 equals 0, which we can factor and get the equation 5x plus 2 times 3x minus 1 equals 0.
00:31
This means that 5 times sine of 2 theta plus 2 equals 0, or 3 times sine of 2 theta minus 1 equals 0, which means that sine of 2 theta is either equal to negative 2 5ths or 1 3rd.
00:50
Putting in inverse sign of negative 2 5ths and 1 3rd into our calculators, we get that 2 theta is negative 23 .6 degrees or 19 .5 degrees.
01:01
For the angle negative 23 .6 degrees that is shown here on this unit circle, and to find the angle for that from 0 to 360, which is this angle, we can do 360 minus 23 .6 and get 336 .4 degrees.
01:26
Another angle that has the same sign value as 19 .5 degrees, which is shown here, is this angle here, which since this is the same as this, we can find by subtracting 19 .5 from 180...
