Posted by **Anonymous** on Friday, April 27, 2012 at 11:59pm.

Question: Trying to find cos π/12, if cos π/6 = square root 3 over 2, how to find cos π/12 using DOUBLE angle formula?

This is what I got so far..

cos 2(π/6) = cos (π/6 + π/6)

= (cos π/6)(cos π/6) - (sin π/6)(sin π/6)

= cos^2 π/6 - sin^2 π/6

Is that right? Please and thank you.

- Trig Help! -
**Reiny**, Saturday, April 28, 2012 at 12:13am
you got it backwards

π/12 = (1/2) of π/6

using cos 2A = cos^2 A - sin^2 A = 2cos^2 A - 1

so cos π/6 = 2 cos^2 π/12 - 1

√3/2 + 1 = 2cos^2 π/12

cos^2 π/12 = √3/4 + 1/2 = (√3 + 2)/4

**cos π/12 = √(√3+2) /2**

check:

by calculator, cos π/12 = .96592...

√(√3+2)/2 = .96592...

My answer is correct.

Of course the answer I gave is not unique

we could have done it this way

cos π/12 = cos 15°

= cos(45-30)°

= cos45cos30 + sin45sin30

= (√2/2)(√3/2) + (√2/2)(1/2) = **(√6 + √2)/4**

which when evaluated is also .96592...

but it asked for a solution using the double angle formula

## Answer This Question

## Related Questions

- Math integrals - What is the indefinite integral of ∫ [sin (π/x)]/ x^...
- Math, please help - Which of the following are trigonometric identities? (Can be...
- Math 2nd question - Express as a single sine or cosine function (note: this is ...
- Precalculus - Use one of the identities cos(t + 2πk) = cos t or sin(t + 2&#...
- Math - Evaluate *Note - We have to find the exact value of these. That I know to...
- Calc - h(x) = {k cos x 0 ≤ x ≤ 9π {13 − x 9π < x ...
- Trig - The set of solution(s) of 2 cos^2 (θ) - 13 cos(θ) + 6 = 0 that ...
- TRIGONOMETRY - Can you check my work, please? This is for a trig study guide for...
- Precalculus - The question(s) are as follows: Given: f(x) = 3cos(3x+π) - 4 ...
- trig - Find all solutions in the interval [0,2π) for cos(x - π/6) = 1...

More Related Questions