use exact values of the sin,cos and tan of (pi/3) and (pi/6)(which I have found)and the symmetry of the graphs of sin,cos and tan to find the exact values of sin(-pi/6), cos(5pi/3) and tan (4pi/3). I know that sin -(pi/6) = -1/2 and cos (5pi/30 = 1/2 and tan 4pi/3 = root 3 but I don't know how to the graphs using excel. I found out the answers using my calculator

To find the exact values of sin(-pi/6), cos(5pi/3), and tan(4pi/3) using the given values and the symmetry of the graphs of sin, cos, and tan, follow these steps:

1. Recall the symmetry properties of the trigonometric functions:
- The sine function is an odd function, which means that sin(-x) = -sin(x).
- The cosine function is an even function, which means that cos(-x) = cos(x).
- The tangent function is an odd function, which means that tan(-x) = -tan(x).

2. Start with sin(-pi/6):
- Since you know that sin(pi/6) = 1/2 from your previous findings, you can use the symmetry property sin(-x) = -sin(x).
- Hence, sin(-pi/6) = -sin(pi/6) = -(1/2) = -1/2.

3. Move on to cos(5pi/3):
- Since you know that cos(pi/3) = 1/2 from your previous findings, you can use the symmetry property cos(-x) = cos(x).
- Hence, cos(5pi/3) = cos(-pi/3) = cos(pi/3) = 1/2.

4. Lastly, consider tan(4pi/3):
- Since you found that tan(pi/3) = sqrt(3) from your previous calculations, you can use the symmetry property tan(-x) = -tan(x).
- Hence, tan(4pi/3) = -tan(-pi/3) = -tan(pi/3) = -(sqrt(3)).

You can verify these results using your calculator or trigonometric identity tables. Concerning graphing the trigonometric functions in Excel, you can use the built-in functions such as SIN, COS, and TAN to plot the respective graphs.