Cofunction Identities Worksheet with Answer Key

What's on the worksheet

1. Decide whether each statement is true.
   \sin\dfrac{\pi}{5} = \cos\dfrac{3\pi}{10}\cos\dfrac{7\pi}{12} = \sin\dfrac{\pi}{12}\sec 110^\circ = \csc(-20^\circ)\csc\dfrac{\pi}{8} = \csc\dfrac{3\pi}{8}\tan\dfrac{2\pi}{9} = \cot\dfrac{5\pi}{18}
2. Write each expression as a single trigonometric function of t or of θ, with a sign if one is needed.
   \csc\left(t + \dfrac{\pi}{2}\right)\tan\left(t - \dfrac{\pi}{2}\right)\cos\left(\dfrac{5\pi}{2} - t\right)\cot\left(\dfrac{3\pi}{2} - t\right)\sin\left(t - \dfrac{3\pi}{2}\right)
3. Find the exact value of each expression without a calculator.
   \cos\dfrac{3\pi}{8}\csc\dfrac{\pi}{8}\sec^2\dfrac{\pi}{5} - \cot^2\dfrac{3\pi}{10}\dfrac{3\cos 112^\circ}{\sin(-22^\circ)}\tan 40^\circ\tan 50^\circ - 2\sin 15^\circ\sec 75^\circ
4. The terminal point of t on the unit circle is P = (513, 1213).
6. A student writes (t - π2) = t "because the cosecant of the complement is the secant."