Find the value of $cos( heta)$ given the angle on the unit circle.
Answer 1
Amelia Mitchell
Given that $\theta = \frac{5\pi}{6}$, find the value of $\cos(\theta)$ on the unit circle.
Step 1: Identify the reference angle.
The reference angle for $\theta = \frac{5\pi}{6}$ is $\pi – \frac{5\pi}{6} = \frac{\pi}{6}$.
Step 2: Determine the sign based on the quadrant.
$\theta = \frac{5\pi}{6}$ is in the second quadrant where cosine is negative.
Step 3: Find the value of cosine for the reference angle.
$\cos(\frac{\pi}{6}) = \frac{\sqrt{3}}{2}$.
Step 4: Apply the sign from step 2.
Therefore, $\cos(\frac{5\pi}{6}) = -\frac{\sqrt{3}}{2}$.
Answer 2
Abigail Nelson
Given that $ heta = frac{7pi}{4}$, find the value of $cos( heta)$ on the unit circle.
Step 1: Identify the reference angle.
The reference angle for $ heta = frac{7pi}{4}$ is $2pi – frac{7pi}{4} = frac{pi}{4}$.
Step 2: Determine the sign based on the quadrant.
$ heta = frac{7pi}{4}$ is in the fourth quadrant where cosine is positive.
Step 3: Find the value of cosine for the reference angle.
$cos(frac{pi}{4}) = frac{1}{sqrt{2}} = frac{sqrt{2}}{2}$.
Step 4: Apply the sign from step 2.
Therefore, $cos(frac{7pi}{4}) = frac{sqrt{2}}{2}$.
Answer 3
Daniel Carter
Find $cos(frac{3pi}{4})$ on the unit circle.
The reference angle is $pi – frac{3pi}{4} = frac{pi}{4}$.
In the second quadrant, cosine is negative.
$cos(frac{pi}{4}) = frac{sqrt{2}}{2}$.
Therefore, $cos(frac{3pi}{4}) = -frac{sqrt{2}}{2}$.
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