Help with compound angle formulae (exact value) for angles over 120 degrees?

1. Apr 22, 2010

misplaced1

1. I don't understand coumpound angle formulae, for example sin(x+y), sin(x-y) etc. I'm supposed to solve using angles in the special triangles--so I use angles like 45, 30, 60, or those angles converted into radians--and add them to get the answer. For example: sin15 would be solved using sin(x-y) or sin (45-30). But when I have a question like "find the exact value of tan165", I'm lost as to what to do.

Question:
Solve the following using exact values:
a)tan165

b)tan 13π/12

2. Relevant Eqns:
tan(x+y)= tanx+tany / 1-tanxtany
tan(x-y)= tanx-tany / 1+tanxtany

3. I'm not at all sure how to go about solving it.

2. Apr 22, 2010

Staff: Mentor

There are only a few angles that have "nice" trig functions that we can represent exactly - 0, 30, 45, 60, and 90 degrees are the ones in the first quadrant. Using the sum and difference formulas and the double-angle and half-angle formulas, we can get a few more.

Notice that 165 degrees = 180 degrees - 15 degrees. Does that suggest an identity that you could use to get the exact value of tan(165 degrees)?

13π/12 = π + π/12, and π/12 = 15 degrees, so tan(13π/12) = tan(π + π/12) = ?

When you say "I don't understand coumpound angle formulae" there's not a whole lot we can do. Do you have any specific questions on these formulas?

3. Apr 23, 2010