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Use the unit eircle to evaluate the six trigonometric functions of 0. 20. 450°

Use the unit eircle to evaluate the six trigonometric functions of 0. 20. 450°

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter2: Right Triangle Trigonometry
Section: Chapter Questions
Problem 5GP
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**Unit Circle Trigonometric Functions Evaluation** ### Instructions: Use the unit circle to evaluate the six trigonometric functions of \( \theta \). ### Problems: 20. \( \theta = 450^\circ \) 21. \( \theta = \frac{3\pi}{2} \) --- **Explanation:** For each given angle: 1. Locate the corresponding point on the unit circle. 2. Determine the coordinates of this point \((x, y)\). 3. Use these coordinates to find the six trigonometric functions: - Sine: \( \sin(\theta) = y \) - Cosine: \( \cos(\theta) = x \) - Tangent: \( \tan(\theta) = \frac{y}{x} \) - Cosecant: \( \csc(\theta) = \frac{1}{y} \) - Secant: \( \sec(\theta) = \frac{1}{x} \) - Cotangent: \( \cot(\theta) = \frac{x}{y} \) ### Important Notes: - Make sure to simplify each function as needed. - Remember that the unit circle has a radius of 1. - The coordinates on the unit circle for standard angles should be memorized or easily referenced. To understand these evaluations fully, please refer to diagrams illustrating the unit circle with critical points marked, such as 0°, 90°, 180°, 270°, and their radian equivalents.
Transcribed Image Text:**Unit Circle Trigonometric Functions Evaluation** ### Instructions: Use the unit circle to evaluate the six trigonometric functions of \( \theta \). ### Problems: 20. \( \theta = 450^\circ \) 21. \( \theta = \frac{3\pi}{2} \) --- **Explanation:** For each given angle: 1. Locate the corresponding point on the unit circle. 2. Determine the coordinates of this point \((x, y)\). 3. Use these coordinates to find the six trigonometric functions: - Sine: \( \sin(\theta) = y \) - Cosine: \( \cos(\theta) = x \) - Tangent: \( \tan(\theta) = \frac{y}{x} \) - Cosecant: \( \csc(\theta) = \frac{1}{y} \) - Secant: \( \sec(\theta) = \frac{1}{x} \) - Cotangent: \( \cot(\theta) = \frac{x}{y} \) ### Important Notes: - Make sure to simplify each function as needed. - Remember that the unit circle has a radius of 1. - The coordinates on the unit circle for standard angles should be memorized or easily referenced. To understand these evaluations fully, please refer to diagrams illustrating the unit circle with critical points marked, such as 0°, 90°, 180°, 270°, and their radian equivalents.
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