Test Your Knowledge: Quadrantal Angle Trig Functions (Pre-Calculus)

📚 Quick Study Guide

• 🧭 Quadrantal Angles: These are angles in standard position (initial side on the positive x-axis) whose terminal side lies on the x-axis or y-axis. Examples include $0^\circ$, $90^\circ$, $180^\circ$, $270^\circ$, and $360^\circ$.
• 📍 Coordinates: On the unit circle, the coordinates for quadrantal angles are:
  • $0^\circ$ (or $0$ radians): $(1, 0)$
  • $90^\circ$ (or $\frac{\pi}{2}$ radians): $(0, 1)$
  • $180^\circ$ (or $\pi$ radians): $(-1, 0)$
  • $270^\circ$ (or $\frac{3\pi}{2}$ radians): $(0, -1)$
  • $360^\circ$ (or $2\pi$ radians): $(1, 0)$
• 📐 Trigonometric Functions: Recall that on the unit circle, for any angle $\theta$, the coordinates are $(\cos \theta, \sin \theta)$. Therefore:
  • $\cos \theta = x$
  • $\sin \theta = y$
  • $\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{y}{x}$
  • $\csc \theta = \frac{1}{\sin \theta} = \frac{1}{y}$
  • $\sec \theta = \frac{1}{\cos \theta} = \frac{1}{x}$
  • $\cot \theta = \frac{\cos \theta}{\sin \theta} = \frac{x}{y}$
• ❗ Undefined Values: Remember that division by zero is undefined. This is important when dealing with tangent, cotangent, secant, and cosecant of quadrantal angles.

Practice Quiz

1. What is the value of $\sin(90^\circ)$?
   1. 0
   2. 1
   3. -1
   4. Undefined
2. What is the value of $\cos(180^\circ)$?
   1. 0
   2. 1
   3. -1
   4. Undefined
3. What is the value of $\tan(270^\circ)$?
   1. 0
   2. 1
   3. -1
   4. Undefined
4. What is the value of $\csc(0^\circ)$?
   1. 0
   2. 1
   3. -1
   4. Undefined
5. What is the value of $\sec(360^\circ)$?
   1. 0
   2. 1
   3. -1
   4. Undefined
6. What is the value of $\cot(90^\circ)$?
   1. 0
   2. 1
   3. -1
   4. Undefined
7. What is the value of $\sin(360^\circ)$?
   1. 0
   2. 1
   3. -1
   4. Undefined