Here are the essential concepts you must grasp in order to answer the question correctly.
Unit Circle
The unit circle is a circle with a radius of one centered at the origin of a coordinate plane. It is fundamental in trigonometry as it provides a geometric interpretation of the sine, cosine, and tangent functions. Angles are measured from the positive x-axis, and the coordinates of points on the circle correspond to the values of these trigonometric functions.
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Introduction to the Unit Circle
Sine Function
The sine function, denoted as sin(θ), represents the y-coordinate of a point on the unit circle corresponding to an angle θ. It is periodic with a period of 360° (or 2π radians), meaning that sin(θ) = sin(θ + 360°n) for any integer n. Understanding the sine function is crucial for evaluating trigonometric values at various angles, including negative angles.
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Graph of Sine and Cosine Function
Negative Angles
Negative angles in trigonometry indicate a clockwise rotation from the positive x-axis. For example, an angle of -270° corresponds to a 270° rotation in the clockwise direction. This concept is important for determining the sine value of angles that exceed 360° or are negative, as it allows us to find equivalent angles within the standard range of 0° to 360°.
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