Algebra 2 Quiz on Exact Trig Values of Special Angles

📚 Quick Study Guide

• 📐 Special Angles: Remember your special angles in degrees: 0°, 30°, 45°, 60°, and 90° (and their radian equivalents: $0$, $\frac{\pi}{6}$, $\frac{\pi}{4}$, $\frac{\pi}{3}$, $\frac{\pi}{2}$).
• 🧭 Unit Circle: Visualize the unit circle. The coordinates of points on the unit circle correspond to (cosine, sine) of the angle.
• 📝 Sine (sin θ): The y-coordinate of the point on the unit circle.
• 📈 Cosine (cos θ): The x-coordinate of the point on the unit circle.
• ➗ Tangent (tan θ): $\tan \theta = \frac{\sin \theta}{\cos \theta}$.
• 🔄 Reciprocal Functions:
  • Cosecant (csc θ) = $\frac{1}{\sin \theta}$
  • Secant (sec θ) = $\frac{1}{\cos \theta}$
  • Cotangent (cot θ) = $\frac{1}{\tan \theta}$ = $\frac{\cos \theta}{\sin \theta}$
• ➕ Signs in Quadrants: Remember which trig functions are positive in each quadrant (ASTC: All, Sine, Tangent, Cosine).

Practice Quiz

1. What is the exact value of $\sin(\frac{\pi}{6})$?
   1. $\frac{1}{2}$
   2. $\frac{\sqrt{2}}{2}$
   3. $\frac{\sqrt{3}}{2}$
   4. $1$
2. What is the exact value of $\cos(\frac{\pi}{4})$?
   1. $\frac{1}{2}$
   2. $\frac{\sqrt{2}}{2}$
   3. $\frac{\sqrt{3}}{2}$
   4. $1$
3. What is the exact value of $\tan(\frac{\pi}{3})$?
   1. $1$
   2. $\frac{\sqrt{3}}{3}$
   3. $\sqrt{3}$
   4. Undefined
4. What is the exact value of $\cos(\frac{\pi}{2})$?
   1. $0$
   2. $1$
   3. $\frac{\sqrt{2}}{2}$
   4. $\frac{\sqrt{3}}{2}$
5. What is the exact value of $\sin(0)$?
   1. $0$
   2. $1$
   3. $\frac{\sqrt{2}}{2}$
   4. $\frac{\sqrt{3}}{2}$
6. What is the exact value of $\sec(\frac{\pi}{3})$?
   1. $\frac{1}{2}$
   2. $2$
   3. $\frac{\sqrt{3}}{2}$
   4. $\frac{2\sqrt{3}}{3}$
7. What is the exact value of $\cot(\frac{\pi}{4})$?
   1. $0$
   2. $1$
   3. $\sqrt{3}$
   4. Undefined