Question

e = radians. Identify the terminal point and tan e.O A. Terminal point: (33) tan = 13B. Terminal point: (1, 1); tan 6 = 73(1,1)tan 0 = 2C. Terminal point:; tane3D. Terminal point:

Answer 1

The correct answer is Option D

This following are the steps to take:

Step1: Convert the angle from radians to degrees

`\begin{gathered} 1\pi radians=180^o \\ \text{Thus }(\pi)/(6)\text{ radians = }(180^o)/(6) \\ \text{ }(\pi)/(6)\text{ radians =}30^o \end{gathered}`

Step 2: Draw a unit circle (with a radius of 1 unit), and show the line which forms angle 30 degrees with the x -axis

Step 3: Compute the values of the terminal points:

`\begin{gathered} Th\text{e x-coordinate of the terminal point = 1 }* cos30^0\text{ = }\frac{\sqrt[]{3}}{2} \\ Th\text{e y-coordinate of the terminal point = 1 }*\sin 30^0\text{ = }(1)/(2) \\ \text{Thus the coordinates of ther terminal point = }(x,y)\text{ = (}\frac{\sqrt[]{3}}{2},\text{ }(1)/(2)\text{)} \end{gathered}`

Step 4: Compute the values of the tangent of the angle:

`\begin{gathered} \tan 30^0\text{ = }(y)/(x)=\frac{(1)/(2)}{\frac{\sqrt[]{3}}{2}}=\frac{1}{\sqrt[]{3}}\text{ } \\ \\ \tan 30^o=\frac{1}{\sqrt[]{3}}\text{ }*\frac{\sqrt[]{3}}{\sqrt[]{3}}\text{ =}\frac{\sqrt[]{3}}{3} \\ \\ \tan 30^{o\text{ }}=\text{ }\frac{\sqrt[]{3}}{3} \end{gathered}`