The unit circle has been divided into twelve equal arcs, corresponding to t-values of 0, π/6, π/3, π/2, 2π/3, 5π/6, π, 7π/6, 4π/3, 3π/2, 5π/3, 11π/6, and 2π
Use the (x,y) coordinates in the figure to find the value of each trigonometric function at the indicated real number, t, or state that the expression is undefined. <IMAGE>
sin 3π/2
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Key Concepts
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 representation of the sine, cosine, and tangent functions. The coordinates of points on the unit circle correspond to the values of these trigonometric functions for various angles measured in radians.
Trigonometric functions, such as sine, cosine, and tangent, relate the angles of a triangle to the lengths of its sides. On the unit circle, the sine of an angle corresponds to the y-coordinate, while the cosine corresponds to the x-coordinate. Understanding these functions is essential for evaluating trigonometric expressions and solving problems involving angles.
Angles in trigonometry can be measured in degrees or radians, with radians being the standard unit in mathematical contexts. One complete revolution around the unit circle is 2Ο radians, and specific angles like Ο/2, Ο, and 3Ο/2 correspond to key points on the circle. Recognizing how to convert between degrees and radians is crucial for accurately determining trigonometric values.