Find the value of $ an$ for given angles on the unit circle
Answer 1
Daniel Carter
Consider the angle $\theta = \frac{3\pi}{4}$ on the unit circle.
First, determine the reference angle. The reference angle for $\frac{3\pi}{4}$ is $\frac{\pi}{4}$.
Since $\frac{3\pi}{4}$ is in the second quadrant, tangent is negative.
We know $\tan \frac{\pi}{4} = 1$, so:
$\tan \frac{3\pi}{4} = -\tan \frac{\pi}{4} = -1$
Answer 2
Emma Johnson
Let’s find the tangent of the angle $ heta = frac{7pi}{6}$.
The reference angle for $frac{7pi}{6}$ is $frac{pi}{6}$.
Since $frac{7pi}{6}$ is in the third quadrant, tangent is positive.
We know $ an frac{pi}{6} = frac{1}{sqrt{3}}$, so:
$ an frac{7pi}{6} = an frac{pi}{6} = frac{1}{sqrt{3}}$
Answer 3
Ella Lewis
To find the tangent of $ heta = frac{5pi}{3}$:
The reference angle is $frac{pi}{3}$.
Since $frac{5pi}{3}$ is in the fourth quadrant, tangent is negative.
We know $ an frac{pi}{3} = sqrt{3}$, so:
$ an frac{5pi}{3} = – an frac{pi}{3} = -sqrt{3}$
Start Using PopAi Today