Math Problem Statement

Check is it’s correct

Check if the coordinates of the terminal points for given arc lengths on the unit circle are correct.

Solution

Let's go over the coordinates in each row and compare them to the unit circle values.

  1. 0: (1,0)(1, 0) — Correct.
  2. π6\frac{\pi}{6}: (32,12)\left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right) — Correct.
  3. π4\frac{\pi}{4}: (22,22)\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right) — Correct.
  4. π3\frac{\pi}{3}: (12,32)\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right) — Correct.
  5. π2\frac{\pi}{2}: (0,1)(0, 1) — Correct.
  6. π\pi: (1,0)(-1, 0) — Correct.
  7. 3π2\frac{3\pi}{2}: (0,1)(0, -1) — Correct.
  8. 2π2\pi: (1,0)(1, 0) — Correct.

All entries are accurate according to the standard unit circle values.

Do you want more details on unit circle coordinates?

Here are 5 follow-up questions to deepen understanding:

  1. What are the coordinates for 5π6\frac{5\pi}{6} on the unit circle?
  2. How do coordinates change as we move counterclockwise around the unit circle?
  3. Why is the unit circle important in trigonometry?
  4. How would you find the coordinates for 7π4\frac{7\pi}{4}?
  5. What is the significance of the reference number in trigonometry?

Tip: Memorizing the unit circle can make solving trigonometric equations easier.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Unit Circle
Radians
Coordinates

Formulas

Coordinates of terminal points on the unit circle

Theorems

Unit Circle Theorem

Suitable Grade Level

Grades 10-12