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 tangent - function value

We know that the tangent function is (y = \tan(x)=\frac{\sin(x)}{\cos(x)}). We need to find the value of (\tan(x)) for some common - angle values of (x).

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}))