Math Problem Statement
Solution
The question asks to find the exact value of using the unit circle. Let's walk through the solution.
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Step 1: Use the unit circle
The angle corresponds to the angle rotated clockwise by radians from the positive x-axis. This leads us to the point on the unit circle. -
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 , the y-coordinate is .
Therefore:
The correct answer is:
- Option A:
Would you like further details on this, or any additional explanations?
Here are five related questions:
- What is ?
- What is ?
- How does the sine function behave for negative angles in general?
- How is the unit circle used to define sine and cosine for angles greater than ?
- What is the sine of ?
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