Visualizing & solving trig equations

uberkrissy · #1 $Old$ November 4th, 2009, 11:06 PM

Find the first 4 positive solutions to each equation. (Use unit circle to make sense of each equation).

1. $sin2\theta=-\frac{1}{2}$

2. $cos2\theta=\sqrt{1-sin^2\theta}$

3. $cos\left [sin^-1 \frac{1}{2}+cos^-1 \frac{-\sqrt{3}}{2} \right ]$

purebladeknight · #2 $Old$ November 5th, 2009, 01:04 AM

Find the first 4 positive solutions to each equation. (Use unit circle to make sense of each equation).

1.

2.

3.

1. is quite easy, just draw a circle and make it go around twice i.e. 720 degrees. and find values in 3rd/4th quad i.e 210. and equate it too 2@ and solve for 4 positive values. 165,105,285,345

2. re-arrange the surd thing to get cos2@=cos@, and draw a graph of both and find intersections that are positive. it seems easier to me than using a circle. 0,120,240,x. i didnt bother drawing the rest up

3. good luck. no idea