Question

Use your understanding of the symmetry of the sine and cosine functions to determine the value of tan(−theta) for all

Answer 1

Answer:

$tan(-\theta)=-tan\theta$

Odd function

Step-by-step explanation:

We are given that

$tan(-\theta)$

We have to determine the value of $tan(-\theta)$and find tangent function is odd,even or neither.

$tan(-\theta)=\frac{sin(-\theta)}{cos(-\theta)}$

$tan\theta=\frac{sin\theta}{cos\theta}$

We know that

$sin(-\theta)=-sin\theta$

$cos(-\theta)=cos\theta$

By using  identities

Then, we get

$tan(-\theta)=\frac{-sin\theta}{cos\theta}=-tan\theta$

$tan(-\theta)=-tan\theta$

Odd function: If $f(-x)=-f(x)$

Even function:If $f(-x)=f(x)$

$tan(-\theta)=-tan\theta$

Therefore, function is an odd function.