which point does the graph of the parent function (y = \tan(x)) pass through?\n(left(\frac{sqrt{3}}{3},\frac{…

which point does the graph of the parent function (y = \tan(x)) pass through?\n(left(\frac{sqrt{3}}{3},\frac{pi}{3}\right))\n(left(\frac{pi}{3},\frac{sqrt{3}}{3}\right))\n(left(\frac{pi}{3},sqrt{3}\right))\n(left(sqrt{3},\frac{pi}{3}\right))

which point does the graph of the parent function (y = \tan(x)) pass through?\n(left(\frac{sqrt{3}}{3},\frac{pi}{3}\right))\n(left(\frac{pi}{3},\frac{sqrt{3}}{3}\right))\n(left(\frac{pi}{3},sqrt{3}\right))\n(left(sqrt{3},\frac{pi}{3}\right))

Answer

Explanation:

Step1: Recall the tangent - function property

The tangent function is defined as $y = \tan(x)=\frac{\sin(x)}{\cos(x)}$. We need to find the value of $y=\tan(x)$ for a given $x$ - value in the options.

Step2: Evaluate $\tan(x)$ at $x = \frac{\pi}{3}$

We know that $\sin(\frac{\pi}{3})=\frac{\sqrt{3}}{2}$ and $\cos(\frac{\pi}{3})=\frac{1}{2}$. Then $\tan(\frac{\pi}{3})=\frac{\sin(\frac{\pi}{3})}{\cos(\frac{\pi}{3})}=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\sqrt{3}$.

Answer:

C. $(\frac{\pi}{3},\sqrt{3})$