SOLUTION: sin 5pi/12

Question 623484: sin 5pi/12
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
I assume the problem is to find this value exactly. Please include the instructions with the problem when you post.

The only exact Trig values come from the special angles. So to find and one of the special angles: 0, , , , and any multiple of these.

One connection (maybe not the only one) is that twelfths are half of sixths. So is 1/2 of . We can use the formula:

(Note: The formula does not usually have the zero. I had to put it there because algebra.com's formula drawing software requires a number in front of a "plus or minus" sign.)

Since is less than it terminates in the first quadrant. Since sin is positive in the first quadrant we know to use the positive square root. So I am going to dispense with the "plus or minus" sign.

Since :

Now we just simplify as much as possible. For , terminates in the second quadrant and the reference angle is . cos is negative in the second quadrant and . So . Inserting this into our formula:

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