how do I work out this trig function?

So what is the problem ? "Look up the answer"? What answer would that be ? You know how to draw a graph don't you ? Just make a table of some angles, 30º, 60º, 90º, and so on, up to 180º. Then double them. Then look up the sine of each angle. Then draw the graph. So you even can get the calculator to do it for you. It ain't exactly rocket science.

You need to memorize the basics about graphing. Then you'll think it's easy.

y = a sin bx; a cos bx

amplitude = |a|

(maximum distance from x-axis)

period = 2π/b

(time to go through 1 full cycle)

critical points every (1/4) period

pattern of critical points, starting when x = 0

sin --> intercept -- maximum -- intercept -- minimum -- intercept

cos --> maximum -- intercept -- minimum -- intercept -- maximum

I'll walk you through this.

y = sin 2θ

amp = 1

pd = π

critical points every π/4

pattern = i - M - i - m - i

Set up a grid for x and y. Label the x-axis in increments of π/4 (2 periods)

0___ π/4 ___ π/2 ___ 3π/4 ___ π ___ 5π/4 ___ 3π/2 ___ 7π/4 ___ 2π

Notice the distance for π. Use that as a distance of approx 3 on the y-axis. Then identify 1 and 2 on the y-axis.

Put in the critical points in the proper pattern and connect.

(0, 0)

(π/4, 1)

(π/2, 0)

(3π/4, -1)

(π, 0)

etc.