Question

Which trigonometric function is an odd function and why?

The cosine function is odd because it is represented by the x-coordinate of the points on the unit circle, and therefore cos(x) = cos(-x).

The sine function is odd because it is represented by the y-coordinate of the points on the unit circle, and therefore sin(-x) = - sin(x).

The cosine function is odd because it is represented by the x-coordinate of the points on the unit circle, and
therefore cos(-x) = cos(x)

The sine function is odd because it is represented by the y-coordinate of the points on the unit circle, and therefore sin(x) = sin(-x).

Answer 1

Answer:

second choice is the answer or it can be

Answer 2

The correct answer is option B.

What is odd function?

"A function $f(x)$ is an odd function when $f(-x)=-f(x)$ ."

For given question,

Consider points A and B on the coordinate plane as shown in following image.

Let, line segment OA makes an angle of $\theta$ with x-axis and ∠COB = $-\theta$

So, the coordinates of points on unit circle with radius 'r' would be, A$(cos \theta, sin\theta)$ and B$(cos(-\theta),sin(-\theta) )$

Let, AC = y, BC = -y and OC = m

Now, consider sine function

$sin\theta=\frac{AC}{OA}$

⇒$sin\theta=\frac{y}{r}$                        ........................(1)

And, $sin(-\theta)=\frac{BC}{OB}$

⇒ $sin(-\theta)=\frac{-y}{r}$

⇒ $sin(-\theta)=-(\frac{y}{r})$             .......................(2)

⇒ $sin(-\theta)=-sin\theta$             ......................(From (1) and (2))

Now, consider cosine function

$cos\theta=\frac{OC}{OA}$

⇒ $cos\theta=\frac{m}{r}$                           ...........................(3)

And, $cos(-\theta)=\frac{OC}{OB}$

⇒ $cos(-\theta)=\frac{m}{r}$                      ...........................(4)

⇒ $cos(-\theta)=cos\theta$                   ...........................(From (3), (4))

Hence, sine function is odd because it is represented by the y-coordinate of the points on the unit circle, and therefore sin(-x) = - sin(x).

Therefore, the correct answer is option B.

Learn more about odd function here,

https://brainly.com/question/14264818

#SPJ2