graph the trig function

And why are you posting this here?

This is just plugging in numbers being sure to set the right units. Hint degrees are not the correct unit.

"show all work" would seem to imply that it is not about plugging in numbers, but about analyzing the function and determining the period, amplitude, phase shift, and offset.

Could be however it was graph this function was the stated problem not analyzing the function or determining any other character of the function.

Use what you know

first its a cosine wave so its a periodic squiggley--its a cosine squiggly so at 0 its 1 and at pi its 0. The midpoint is1

second is a negative cosine squiggley--so the normal cosine squiggley is upside down

third it has a 3 term in the variable t, so the frequency is tripled , normal wavelength of a cosine squiggley is 2pi, but if 3t=2pi, then wavelength is 2pi/3.

fourth its been displaced at -cos(0)=-1 0=pi/4-3to so to=pi/12 so the t axis is shifted to the right by pi/12

fifth the cos is negative--since cos is a even function the cosine wave is reflected about the to line (i.e. do nothing past step 4)

rap