Expert: Steve Holleran - 9/11/2007

Question
Solve the following trigonometric equations.
Give all positive values of the angle between 0�‹ and 360�‹ that will satisfy each.
Give any approximate value to the nearest minute only.


3) Sin(2theta) = �ã3/2

4) Sin(2x) - Cos(x) = 0

5) Sin(2x - 10�‹) = 1/2  

Answer
Hi Charles,

On #3, I can't make out what's in front of the "3" on the right side; its some weird symbol, so I don't know the value there.


On #4, use the double-angle identity for sin 2x:

              sin 2x = 2 * sin x * cos x

then   2 * sin x * cos x - cos x = 0

factor out a cos x:

               cos x ( 2 sin x - 1) = 0

so       cos x = 0          or   2 sin x - 1 = 0

so         x = 90, 270             sin x = 1/2

                                   x = 30, 150


#5) I hope the angle here is "2x-10".  There's something after the 10, but I don't understand it, and hope its just a typo.  If so, here's what I'd do:

           sin(2x - 10) = 1/2

so             2x - 10 = 30  or 2x - 10 = 150

                2x = 40     or     2x = 160

                 x = 20     or       x = 80

Hope this helps out.

Steve Holleran