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irga5000 [103]
1 year ago
15

Show that tangent is an odd function.Use the figure in your proof.

Mathematics
1 answer:
svlad2 [7]1 year ago
7 0

We have to prove that the tangent is an odd function.

If the tangent is an odd function, the following condition should be satisfied:

\tan(t)=-\tan(-t)

From the figure we can see that the tangent can be expressed as:

We can start then from tan(t) and will try to arrive to -tan(-t):

\begin{gathered} \tan(t)=\frac{\sin(t)}{cos(t)}=\frac{y}{x} \\ \tan(t)=\frac{-(-y)}{x}=\frac{-\sin(-t)}{\cos(-t)} \\ \tan(t)=-\frac{\sin(-t)}{\cos(-t)} \\ \tan(t)=-\tan(-t) \end{gathered}

We have arrived to the condition for odd functions, so we have just proved that the tangent function is an odd function.

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