Math / Trigonometry

Questioncosine and cotangent of $\frac{\pi}{3}$

Studdy Solution

STEP 1

1. We are working with trigonometric functions and angles measured in radians.
2. The angle $\frac{\pi}{3}$ is a standard angle for which trigonometric values are commonly known.

STEP 2

1. Calculate the cosine of $\frac{\pi}{3}$ .
2. Calculate the cotangent of $\frac{\pi}{3}$ .

STEP 3

To find $\cos\left(\frac{\pi}{3}\right)$ , recall the value from the unit circle or trigonometric tables. The cosine of $\frac{\pi}{3}$ is:
$\cos\left(\frac{\pi}{3}\right) = \frac{1}{2}$

STEP 4

To find $\cot\left(\frac{\pi}{3}\right)$ , we use the identity $\cot(\theta) = \frac{1}{\tan(\theta)}$ . First, find $\tan\left(\frac{\pi}{3}\right)$ .
The tangent of $\frac{\pi}{3}$ is:
$\tan\left(\frac{\pi}{3}\right) = \sqrt{3}$
Now, calculate the cotangent:
$\cot\left(\frac{\pi}{3}\right) = \frac{1}{\tan\left(\frac{\pi}{3}\right)} = \frac{1}{\sqrt{3}}$
The values are: $\cos\left(\frac{\pi}{3}\right) = \frac{1}{2}$ $\cot\left(\frac{\pi}{3}\right) = \frac{1}{\sqrt{3}}$

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