I need help finding the exact value of cos(pi/12)?

Question

I want to use the sum or difference identity for cosine

Answer 1

pi/12 = pi/3-pi/4
so cos(pi/12) = 1/4*sqrt(2)+1/4sqrt(6)= 1/4( sqrt 2+sqrt6)

Answer 2

(pi/12)=15 degrees


Problem: Find cos (15degrees).

Solution: Write 15 degrees in terms of
angles with known trig. ratio values.

cos (45 - 30)

Use the cosine identity to
rewrite the expression.

(cos 45)cos 30 + (sin 45)sin 30

Using the values you know for the trig.
ratios of special angles, rewrite the
expression.

SQRT(2)/2 * SQRT(3)/2 + SQRT(2)/2 * 1/2


Perform the indicated multiplications.

SQRT(6)/4 + SQRT(2)/4

(( SQRT(6) + SQRT(2)))/4

At this point, you can convert your answer back to radians if necessary.

There is also a cosine identity for a sum of angles. It is shown below.

cos (A + B) = (cos A)cos B - (sin A)sin B

Answer 3

Cos 2x = 2cos^x - 1

Let x = pi/12

Cos pi/6 = (sqrt3)/2 = 2 cos^2 pi/12 - 1

Rearrange:

((sqrt3)/2 + 1)/2 = cos^2 pi/12

cos pi/12 = sqrt[((sqrt3)/2 + 1)/2]

= 0.9659

Answer 4

cos(pi/12) = cos(15º) = cos(45º - 30º)

= cos(45º)*cos(30º) + sin(45º)*sin(30º)

= [sqrt(2) / 2][sqrt(3) / 2] + [sqrt(2) / 2][1 / 2]

= sqrt(6) / 4 + sqrt(2) / 4

= [sqrt(6) + sqrt(2)] / 4