Unit Circle Trig Quiz
Precalculus • Trigonometry Unit Circle Foundations
Score: ______ / 36 pts
Unit Circle Trig Quiz
Evaluating All Six Trigonometric Functions
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Date:
Period:
Directions: Give all answers as exact values simplified in radical form with rationalized denominators. Write undefined where a function has no real value. Show terminal coordinates \((x,y)\) and reference angles for full credit.
1 Part 1: Unit Circle Ratio Definitions
(6 points • 1 pt each)
Let \(P(x, y)\) be the point of intersection between the terminal side of angle \(\theta\) and the unit circle \(x^2 + y^2 = 1\). Write each trigonometric function in terms of \(x\) and/or \(y\).
\(\sin \theta =\)
\(\cos \theta =\)
\(\tan \theta =\)
\(\csc \theta =\)
\(\sec \theta =\)
\(\cot \theta =\)
Problem 1 \(\theta = \dfrac{\pi}{3}\) \(\quad (60^\circ)\)
Quadrant I Special Angle • 6 points
Ref \(\theta'\):
Terminal \((x, y)\):
\(\sin \frac{\pi}{3} =\)
\(\csc \frac{\pi}{3} =\)
\(\cos \frac{\pi}{3} =\)
\(\sec \frac{\pi}{3} =\)
\(\tan \frac{\pi}{3} =\)
\(\cot \frac{\pi}{3} =\)
Problem 2 \(\theta = \dfrac{3\pi}{2}\) \(\quad (270^\circ)\)
Quadrantal Angle (Negative \(y\)-axis) • 6 points
Quadrant/Axis:
Terminal \((x, y)\):
\(\sin \frac{3\pi}{2} =\)
\(\csc \frac{3\pi}{2} =\)
\(\cos \frac{3\pi}{2} =\)
\(\sec \frac{3\pi}{2} =\)
\(\tan \frac{3\pi}{2} =\)
\(\cot \frac{3\pi}{2} =\)
Unit Circle Trig Quiz • Precalculus Page 1 of 2
Unit Circle Trig Quiz • Quadrants II, III, & IV
Student Name:
Page 2
Problem 3 \(\theta = \dfrac{3\pi}{4}\) \(\quad (135^\circ)\)
Quadrant II Angle • 6 points
Ref \(\theta'\):
Terminal \((x, y)\):
\(\sin \frac{3\pi}{4} =\)
\(\csc \frac{3\pi}{4} =\)
\(\cos \frac{3\pi}{4} =\)
\(\sec \frac{3\pi}{4} =\)
\(\tan \frac{3\pi}{4} =\)
\(\cot \frac{3\pi}{4} =\)
Problem 4 \(\theta = \dfrac{7\pi}{6}\) \(\quad (210^\circ)\)
Quadrant III Angle • 6 points
Ref \(\theta'\):
Terminal \((x, y)\):
\(\sin \frac{7\pi}{6} =\)
\(\csc \frac{7\pi}{6} =\)
\(\cos \frac{7\pi}{6} =\)
\(\sec \frac{7\pi}{6} =\)
\(\tan \frac{7\pi}{6} =\)
\(\cot \frac{7\pi}{6} =\)
Problem 5 \(\theta = \dfrac{11\pi}{6}\) \(\quad (330^\circ)\)
Quadrant IV Angle • 6 points
Ref \(\theta'\):
Terminal \((x, y)\):
\(\sin \frac{11\pi}{6} =\)
\(\csc \frac{11\pi}{6} =\)
\(\cos \frac{11\pi}{6} =\)
\(\sec \frac{11\pi}{6} =\)
\(\tan \frac{11\pi}{6} =\)
\(\cot \frac{11\pi}{6} =\)
Unit Circle Trig Quiz • Precalculus Page 2 of 2
