Quiz on Basic Trigonometric Ratios and Unit Circle Values

📚 Quick Study Guide

• 📐 Trigonometric Ratios: For a right triangle with angle $\theta$, we define the trigonometric ratios as follows:
  • 🔍 Sine: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$
  • 💡 Cosine: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$
  • 📝 Tangent: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$
• 🧭 Reciprocal Ratios:
  • 🔑 Cosecant: $\csc(\theta) = \frac{1}{\sin(\theta)}$
  • 🔒 Secant: $\sec(\theta) = \frac{1}{\cos(\theta)}$
  • 📌 Cotangent: $\cot(\theta) = \frac{1}{\tan(\theta)}$
• ⏺️ Unit Circle: A circle with radius 1 centered at the origin. It's used to find trigonometric values for any angle.
  • $\cos(\theta)$ corresponds to the x-coordinate of the point on the unit circle.
  • $\sin(\theta)$ corresponds to the y-coordinate of the point on the unit circle.
• 📈 Key Unit Circle Values: Some common values to remember:
  • 0° (0 radians): $\sin(0) = 0$, $\cos(0) = 1$
  • 30° ($\frac{\pi}{6}$ radians): $\sin(\frac{\pi}{6}) = \frac{1}{2}$, $\cos(\frac{\pi}{6}) = \frac{\sqrt{3}}{2}$
  • 45° ($\frac{\pi}{4}$ radians): $\sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$, $\cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$
  • 60° ($\frac{\pi}{3}$ radians): $\sin(\frac{\pi}{3}) = \frac{\sqrt{3}}{2}$, $\cos(\frac{\pi}{3}) = \frac{1}{2}$
  • 90° ($\frac{\pi}{2}$ radians): $\sin(\frac{\pi}{2}) = 1$, $\cos(\frac{\pi}{2}) = 0$

🧪 Practice Quiz

1. Question 1: What is the value of $\sin(\frac{\pi}{2})$?
   1. A) 0
   2. B) 1
   3. C) $\frac{1}{2}$
   4. D) $\frac{\sqrt{2}}{2}$
2. Question 2: What is the value of $\cos(\frac{\pi}{3})$?
   1. A) 0
   2. B) 1
   3. C) $\frac{1}{2}$
   4. D) $\frac{\sqrt{3}}{2}$
3. Question 3: If $\tan(\theta) = 1$, what could be the value of $\theta$ in radians?
   1. A) 0
   2. B) $\frac{\pi}{2}$
   3. C) $\frac{\pi}{4}$
   4. D) $\frac{\pi}{3}$
4. Question 4: What is the value of $\sin(\frac{\pi}{6})$?
   1. A) $\frac{\sqrt{3}}{2}$
   2. B) $\frac{\sqrt{2}}{2}$
   3. C) $\frac{1}{2}$
   4. D) 1
5. Question 5: What is the value of $\cos(0)$?
   1. A) 0
   2. B) 1
   3. C) $\frac{1}{2}$
   4. D) $\frac{\sqrt{2}}{2}$
6. Question 6: What is the value of $\csc(\frac{\pi}{2})$?
   1. A) 0
   2. B) 1
   3. C) 2
   4. D) Undefined
7. Question 7: What is the value of $\sec(0)$?
   1. A) 0
   2. B) 1
   3. C) 2
   4. D) Undefined