Use the exact values of the sin, cos and tan of pi/3 and pi/6, and the symmetry of the graphs of sin, cos and tan, to find the exact values of sin

Question

-pi/6, cos 5/3pi and tan 4pi/3.
I have found the answers to the first three using the special tables
sin pi/6 = cos pi/3 = 1/2
cos pi/6 = sin pi/3 = �root 3/2
tan pi/3 = �root 3
tan pi/6 = 1/�root 3
I know that the symmetry of sin(-pi/6 is in the third quadrant, so 7pi/6 =
- 0.5
the symmetry of cos 5pi/3 i have taken 2pi - 5pi/3 to give cos pi/3 = 0.5 but i am not too sure where the symmetry comes in
With the tan I do not quite know where to start. Maybe pi + pi/3.
As for plotting the graphs of sin,cos and tan; I do not know where to start here using the pi radians (whereas as usually I am good at plotting graphs. (perhaps it is an age thing :-(

Answer 1

tan 4 pi/3 is in quadrant three pi/3 or 60 degrees below the -x axis
so
both x and y are negative
tan (pi+pi/3) = tan (60 deg) = sqrt(3)

Answer 2

Can anyone give me some pointers on how to plot the graph in excel please