How to graph trig without a calculator??

Sorry about the double post, no idea how that happened.

How to graph trig without a calculator?

The question:

Graph the following without using a graphing program:

y = 2 cos ( 2 x- 90^{0 }) (Thats 90 degrees)

The lesson I was given contains a very small explanation that is basically useless. So I'm not really sure how to start this..

Re: How to calculate magnitude?

So y= cos(2(x- 45)). This problem looks like it expects you to know how to work with a "general sinusoidal function". Since cosine of any number lies between -1 and 1, this function will always lie between -2 and 2. Cosine has period $\displaystyle 360$ degrees but when $\displaystyle 2x= 360$, $\displaystyle x= 180$ so this function has period $\displaystyle 180$ degrees. Finally, cos(0)= 1 and 2x- 90= 2(x- 45)= 0 when x= 45.

So I would do this: Draw two horizontal lines at y= -2 and y= 2 to give the boundaries. Start at the upper line at x= 45. 45+ 180= 225 so mark (225, 2). The 180 interval divides into 4 sections: 180/4= 45 so at x= 45+ 45= 90, we are at 0, at 90+ 45= 135 down to -2, at 135+ 45= 180, up to 0 again, at 180+ 45= 225 up to 2 again, completing the cycle.