Question

find the exact value of cos(pi/12)

Answer 1

Use a calculator.

Answer 2

can't use a calculator, pi is a non repeating number, so a decimal wouldn't give and Exact value.

Answer 3

i have to show the work

Answer 4

hint, remember the unit circle.

Answer 5

use the difference of 2 angles

\[\cos(A - B)\] where A = pi/3 and B = pi/4

both the values A and B have exact values.

So after you have written the difference in expanded form, make the approriate substitutions.

Answer 6

the answer is \[\frac{ \sqrt{6} }{ 4 } + \frac{ \sqrt{2} }{ 4 }\] but i need to know how to get there
\[\frac{ \sqrt{6} }{ 4 } + \frac{ \sqrt{2} }{ 4 }\]

Answer 7

hope it makes sense.

Answer 8

not really :/

Answer 9

ok... do you know the expansion for cos(A - B)..?

Answer 10

no... im taking precal but i really don't get anything

Answer 11

the reason you need it is because

\[\frac{\pi}{3} - \frac{\pi}{4} = \frac{\pi}{12}\]

Answer 12

well this is the expansion

\[\cos(A -B) = \cos(A)\cos(B) - \sin(A)\sin(B)\]

so if \[A = \frac{\pi}{3}...and.... B=\frac{\pi}{4}\]

you'll have

\[\cos(\frac{\pi}{12})=\cos(\frac{\pi}{3} - \frac{\pi}{4}) = \cos(\frac{\pi}{3})\cos(\frac{\pi}{4}) - \sin(\frac{\pi}{3})\sin(\frac{\pi}{4})\]

now you have trig ratios and angles that have exact values... make the necessary substitution... and then evaluate for the answer

Answer 13

opps should be a + between the terms not a negative

\[\cos(\frac{\pi}{3})\cos(\frac{\pi}{4} )+ \sin(\frac{\pi}{3})\sin(\frac{\pi}{4})\]

Answer 14

[0.35+\sqrt{6}/4\]