If the terminal side of an angle θ intersects the unit circle at ($\frac{\sqrt{3}}{2}$, $\frac{1}{2}$),...

Question

1. If the terminal side of an angle θ intersects the unit circle at ($\frac{\sqrt{3}}{2}$, $\frac{1}{2}$), what is tan(θ)?
a. $\frac{1}{2}$
b. $\frac{\sqrt{3}}{3}$
c. $\frac{\sqrt{3}}{2}$
d. $\sqrt{3}$
2. What is tan($\frac{\pi}{2}$)?
a. undefined
b. 1
c. −1
d. 0

SnapAndSolve AI · Accepted Answer

The tangent of an angle θ in the unit circle is given by the ratio of the y-coordinate to the x-coordinate. Therefore, tan(θ) = $\frac{1/2}{\sqrt{3}/2}$ = $\frac{1}{\sqrt{3}}$ = $\frac{\sqrt{3}}{3}$. The correct answer is b. $\frac{\sqrt{3}}{3}$.
The tangent of $\frac{\pi}{2}$ is undefined because the cosine of $\frac{\pi}{2}$ is 0, and division by zero is undefined. The correct answer is a. undefined.

contact us

Contact Info

If the terminal side of an angle θ intersects the unit circle at (\(\frac{\sqrt{3}}{2}\), \(\frac{1}{2}\)),...

Answer

Have a similar question?

More math questions