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Section 4.2 – Trigonometric Functions: The Unit Circle

Section Details.
  • Using the unit circle to define the six trigonometric functions
  • Memorizing the points on the unit circle corresponding to the common angles and using them to evaluate the trigonometric functions at the common angles
  • Properties of the trigonometric functions

Practice Problems

Directions. The following are review problems for the section. We recommend you work the problems yourself, and then click "Answer" to check your answer. If you do not understand a problem, you can click "Video" to learn how to solve it. 
Evaluate the six trigonometric functions for the following angles: 
a. ​\(\sin \dfrac{4\pi}{3}\) g. ​\(\sin 315^\circ\)
b. ​\(\cos \dfrac{4\pi}{3}\) h. \(\cos 315^\circ\)
c. \(\tan \dfrac{4\pi}{3}\) i. ​\(\tan 315^\circ\)
d. ​\(\cot \dfrac{4\pi}{3}\) j. ​\(\cot 315^\circ\)
e. \(\sec \dfrac{4\pi}{3}\) k. \(\sec 315^\circ\)
f. ​\(\csc \dfrac{4\pi}{3}\) l. ​\(\csc 315^\circ\)

a. \(\sin\dfrac{4\pi}{3}=\dfrac{\sqrt{3}}{2}\) g. \(\sin315^\circ=-\dfrac{\sqrt{2}}{2}\)
b. \(\cos\dfrac{4\pi}{3}=\dfrac{1}{2}\) h. \(\cos315^\circ=\dfrac{\sqrt{2}}{2}\)
c. \(\tan\dfrac{4\pi}{3}=\sqrt{3}\) i. \(\tan315^\circ=-1\)
d. \(\cot\dfrac{4\pi}{3}=\dfrac{1}{\sqrt{3}}\) j. \(\cot315^\circ=-1\)
e. \(\sec\dfrac{4\pi}{3}=2\) k. \(\sec315^\circ=\sqrt{2}\)
f. \(\csc\dfrac{4\pi}{3}=\dfrac{2}{\sqrt{3}}\) l. \(\csc315^\circ=-\sqrt{2}\)