Math Problem Statement

Use the unit circle, along with the definitions of the circular functions, to find the exact values for the given functions when s = -π.

Solution

The question asks to find the exact value of sin(π)\sin(-\pi) using the unit circle. Let's walk through the solution.

  1. Step 1: Use the unit circle
    The angle π-\pi corresponds to the angle rotated clockwise by π\pi radians from the positive x-axis. This leads us to the point (1,0)(-1, 0) on the unit circle.

  2. Step 2: Recall the sine function
    The sine of an angle in the unit circle is the y-coordinate of the corresponding point. In this case, at π-\pi, the y-coordinate is 00.

Therefore: sin(π)=0\sin(-\pi) = 0

The correct answer is:

  • Option A: sin(π)=0\sin(-\pi) = 0

Would you like further details on this, or any additional explanations?

Here are five related questions:

  1. What is cos(π)\cos(-\pi)?
  2. What is tan(π)\tan(-\pi)?
  3. How does the sine function behave for negative angles in general?
  4. How is the unit circle used to define sine and cosine for angles greater than 2π2\pi?
  5. What is the sine of π2-\frac{\pi}{2}?

Tip: Remember that sine of any angle corresponds to the y-coordinate of the point on the unit circle, while cosine corresponds to the x-coordinate.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Unit Circle
Sine Function

Formulas

sin(θ) = y-coordinate of point on unit circle
cos(θ) = x-coordinate of point on unit circle

Theorems

Unit Circle Theorem
Trigonometric Function Properties

Suitable Grade Level

Grades 10-12