Math Problem Statement

Drag each trigonometric function to the correct location on the chart. Match the trigonometric functions with their values.

Solution

The task involves matching trigonometric values with their functions. Let's solve it step-by-step:

Step 1: Recall the basic values of sine and cosine for common angles:

  1. sinπ6=12=0.5\sin \frac{\pi}{6} = \frac{1}{2} = 0.5
  2. sinπ3=32\sin \frac{\pi}{3} = \frac{\sqrt{3}}{2}
  3. cosπ6=32\cos \frac{\pi}{6} = \frac{\sqrt{3}}{2}
  4. cosπ3=12=0.5\cos \frac{\pi}{3} = \frac{1}{2} = 0.5

Step 2: Match each function to its value:

  • sinπ6\sin \frac{\pi}{6}: 0.50.5
  • sinπ3\sin \frac{\pi}{3}: 32\frac{\sqrt{3}}{2}
  • cosπ6\cos \frac{\pi}{6}: 32\frac{\sqrt{3}}{2}
  • cosπ3\cos \frac{\pi}{3}: 0.50.5

Step 3: Place the functions accordingly in the chart:

  • Place sinπ6\sin \frac{\pi}{6} and cosπ3\cos \frac{\pi}{3} on 0.5.
  • Place sinπ3\sin \frac{\pi}{3} and cosπ6\cos \frac{\pi}{6} on 32\frac{\sqrt{3}}{2}.

If you have further questions or want explanations for other trigonometric concepts, let me know!

Here are 5 related questions to expand your understanding:

  1. How do sine and cosine functions relate to the unit circle?
  2. What are the values of sine and cosine at π/4\pi/4?
  3. Can you explain the difference between sine and cosine graphically?
  4. What are the reciprocal trigonometric functions of sine and cosine?
  5. How do trigonometric values change in different quadrants?

Tip: Memorizing the sine and cosine values for π6\frac{\pi}{6}, π3\frac{\pi}{3}, and π4\frac{\pi}{4} will help you solve many trigonometric problems quickly.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Trigonometry
Unit Circle Values
Sine and Cosine Functions

Formulas

sin(π/6) = 1/2 = 0.5
sin(π/3) = √3/2
cos(π/6) = √3/2
cos(π/3) = 1/2 = 0.5

Theorems

Values of trigonometric functions based on standard angles in the unit circle

Suitable Grade Level

Grades 10-12