Question

find the exact value of cos 15 degrees

Answer 1

use a cos difference identity

Answer 2

Cos(45 degrees)-Cos(30 degrees)

Answer 3

Yup.

Answer 4

no cos(45-30)

Answer 5

That's what i meant. Sorry!

Answer 6

do you knwo your cos difference identity?

Answer 7

And do you know your unique angles? (30, 45, 60, and 90)?

Answer 8

\[\cos(A-B)=CosACosB+SinASinB \]

Answer 9

wait. i thought you were the op lol. i guess we should wait for the op

Answer 10

Heheh.

Answer 11

waitt.... i know how to do this...

Answer 12

i hope so.

Answer 13

CALCULATOR

Answer 14

that is a complete disservice to your education.

Answer 15

LOL...u never mentioned which method to use...this is just me using my intelligence

Answer 16

because it isnt my question. i know how to solve it. they will find calculus much easier if they can get identies down.

Answer 17

Why is this still open?

Answer 18

\[
\cos^2(x) = \frac{1+\cos(2x)}{2}
\]In our case: \[
\cos^2(15) = \frac{1+\cos(30)}{2}
\]

Answer 19

This means \[
|\cos^2(15)| = \sqrt{\frac{1+\cos(30)}{2}}
\]We can tell that \(15\) is in the first quadrant, so our answer should be positive.

Answer 20

For a 30 degree right angle, first imagine an equilateral triangle with 60 degrees in each angle.

Answer 21

Cut it in half, and realize that you have two 30 degree angles.

Answer 22

It's clear that the hypotenuse is twice the length of the opposite side.

So since \[
hypotenuse^2 = adjacent^2+opposite^2
\]We can say: \[
hypotenuse^2 = adjacent^2 + \left(\frac{hypotenuse}{2}\right)^2
\]

Answer 23

Remember that \(\cos(x) = \frac{adjacent}{hypotenuse}\).
If we let \(hypotenuse = 1\), then \(\cos(x) = adjacent\).

Answer 24

So \[
1^2 = adjacent^2 + \left(\frac{1}{2}\right)^2
\]Or \[
adjacent^2 = 1 - \frac{1}{4}
\]Solving for the adjacent side, we get: \[
adjacent = \sqrt{\frac{3}{4}} = \frac{\sqrt 3}{2}
\]

Answer 25

In short: \(\cos(30^\circ) = \frac{\sqrt 3}{2}\)