Proof of Trigonometric Identities: Sin(-theta), Cos(-theta), Tan(-theta)

[Miike012]

Homework Statement

Can some one please give me the proof or somewhere I can find the proof or just an explanation why

Sin(-theta) = -Sin(theta
Cos(-theta) = cos(theta)
Tan(-theta)= -Tan(theta)

Thank you..

Homework Equations

The Attempt at a Solution

 

[osnarf]

You can see the result for sine and cosine easily if you graph them. If you want a more analytic approach you can use the periodicy.

Once you figure out why it's true for sine and cosine, you can use the tangent's relationship with the sine and cosine to see why the third result is true.

 

[symbolipoint]

Examine the Right-triangle values on the Unit Circle.