We want to show that f(-t)=-f(t)f(-t)= sin (−t) = −y = −sin t = −f(t) and thus the sine function is odd.∎Now you should show that cosine is an even function and tangent is an odd function is asimilar manner. You should use the above figure in your proof.1. Statement: Show that cosine is an even function.2. Statement: Show that tangent is an odd function.3. Derivation: Derive a formula for cos 3 theta , in terms of cos theta and sin theta or just cos theta. Recall the following definitions from algebra regarding even and odd functions:• A function f(x) is even if f(-x) = f(x) for each x in the domain of f.• A function f(x) is odd if f(-x) = −f(x) for each x in the domain of f.Also note that the graph of an even function is symmetric about the y-axis and the graphof an odd function is symmetric about the origin.The following proof shows that sine is an odd function. Use it as a model to prove thatcosine is an even function and that tangent is an odd function.Statement: Show that sine is an odd function.Proof: Let f (t) = sint and consider the following figure:y(x,y)t(x,-y)x

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We want to show that f(-t)=-f(t) f(-t)= sin (−t) = −y = −sin t = −f(t) and thus the sine function is odd. ∎ Now you should show that cosine is an even function and tangent is an odd function is a similar manner. You should use the above figure in your proof. 1. Statement: Show that cosine is an even function. 2. Statement: Show that tangent is an odd function. 3. Derivation: Derive a formula for cos 3 theta , in terms of cos theta and sin theta or just cos theta.