# How do you find the exact values of cos 15 using the half angle formula?

Then teach the underlying concepts
Don't copy without citing sources
preview
?

Write a one sentence answer...

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

Describe your changes (optional) 200

21
Aug 30, 2015

$\textcolor{red}{\cos 15 = \frac{\sqrt{2 + \sqrt{3}}}{2}}$

#### Explanation:

The cosine half-angle formula is

cos(x/2) = ±sqrt((1 + cos x) / 2)

The sign is positive if $\frac{x}{2}$ is in the first or fourth quadrant and negative if $\frac{x}{2}$ is in the second or third quadrant.

15° is in the first quadrant, so the sign is positive.

$15 = \frac{30}{2}$

$\cos 15 = \cos \left(\frac{30}{2}\right) = \sqrt{\frac{1 + \cos 30}{2}}$

$\cos 15 = \sqrt{\frac{1 + \frac{\sqrt{3}}{2}}{2}} = \sqrt{\frac{2 + \sqrt{3}}{4}}$

$\cos 15 = \frac{\sqrt{2 + \sqrt{3}}}{2}$

##### Just asked! See more
• 23 minutes ago
• 23 minutes ago
• 24 minutes ago
• 27 minutes ago
• 13 seconds ago
• A minute ago
• 5 minutes ago
• 7 minutes ago
• 15 minutes ago
• 23 minutes ago
• 23 minutes ago
• 23 minutes ago
• 24 minutes ago
• 27 minutes ago