Find the values of $cos( heta)$ on the unit circle
Answer 1
Thomas Walker
Consider the unit circle where the radius is 1. Identify the angles $\theta$ where $\cos(\theta) = \frac{1}{2}$.
Step 1: Recall the unit circle and the corresponding cosine values for common angles.
Step 2: Evaluate the cosine values: $\cos(60^\circ) = \frac{1}{2}$ and $\cos(300^\circ) = \frac{1}{2}$.
Step 3: Convert these angles to radians: $60^\circ = \frac{\pi}{3}$ and $300^\circ = \frac{5\pi}{3}$.
Therefore, the values of $\theta$ where $\cos(\theta) = \frac{1}{2}$ are $\frac{\pi}{3}$ and $\frac{5\pi}{3}$.
Answer 2
Alex Thompson
To find the values of $cos( heta)$ that equal $frac{1}{2}$ on the unit circle:
Step 1: Recognize that $cos( heta) = frac{1}{2}$ corresponds to specific angles.
Step 2: From the unit circle, $cos( heta) = frac{1}{2}$ at $ heta = 60^circ$ and $ heta = 300^circ$.
Step 3: Convert these degree measures to radians: $ heta = frac{pi}{3}$ and $ heta = frac{5pi}{3}$.
Therefore, $ heta = frac{pi}{3}$ and $ heta = frac{5pi}{3}$ are the angles where $cos( heta) = frac{1}{2}$.
Answer 3
Emily Hall
Locate angles $ heta$ on the unit circle where $cos( heta) = frac{1}{2}$:
In degrees: $60^circ$ and $300^circ$.
Convert to radians: $frac{pi}{3}$ and $frac{5pi}{3}$.
These angles where $cos( heta) = frac{1}{2}$ are $frac{pi}{3}$ and $frac{5pi}{3}$.
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