Question

use sum or difference formulas to find the exact value of each trigonometric function. tan 23pie/12

Answer 1

You want to write 23pi/12 as a sum (in this case) by finding two numbers that sum to 23 that also simplify with the 12 so that you end up with a denominator of 2, 3, 4, or 6. Can you try to do that?

Answer 2

so i have to have one that has the greatest common factor?

Answer 3

Start by subtracting even numbers from 23 and looking for even numbers as an answer.

Answer 4

For example, 23 - 6 = 17 so that does not work because the 17 will not simplify with the 12, but 23 - 8 = 15 (whoops, not even!) and that seems to work since they both will reduce 8pi/12 + 15pi/12

Answer 5

Btw, earlier I should have said "even" or a multiple of 3 since even numbers and 3 (and its multiples) will divide the 12.

Answer 6

Once you reduce the 8pi/12 and the 15pi/12 you use the tangent of a sum identity. I assume you know or have it as reference.

Answer 7

The identity is

Answer 8

Give it a try. The answer is \[\sqrt{3}-2\]

Answer 9

are you sure?

Answer 10

I think so. What did you get?

Answer 11

I didn't actually solve using the identity. I used http://www.wolframalpha.com/input/?i=tan%2823pi%2F12%29

Answer 12

are you positive?