Question

Express each angle as a compound angle, using a pair of angles from the special triangles

a) 75 degrees
b) pie over 12
c) 5 pie over 6

Answer 1

The special triangles are 30-60-90 and 45-45-90.

So

a) 75 degrees = 45 degrees + 30 degrees

b) $\frac{\pi}{12} = \frac{\pi}{4} - \frac{\pi}{6}$

The same as 15 degrees = 45 degrees – 30 degrees

c) $\frac{5\pi}{6} = \frac{\pi}{2} +\frac{\pi}{3}$

The same as 150 degrees = 90 degrees + 60 degrees