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### Trigonometric Functions on the Unit Circle A point \( P(x, y) \) is shown on the unit circle corresponding to a real number \( t \). Find the values of the trigonometric functions at \( t \). The point \( P \) is \( \left(\frac{15}{17}, \frac{8}{17}\right) \). **Questions:** a. \( \sin t = \) [Type an integer or a simplified fraction.] b. \( \cos t = \) [Type an integer or a simplified fraction.] c. \( \tan t = \) [Type an integer or a simplified fraction.] d. \( \csc t = \) [Type an integer or a simplified fraction.] e. \( \sec t = \) [Type an integer or a simplified fraction.] f. \( \cot t = \) [Type an integer or a simplified fraction.] **Diagram Description:** The diagram depicts a unit circle centered at the origin \((0,0)\) on the coordinate plane. The circle is highlighted with a radius reaching point \( P \) on the circle's circumference. The angle \( t \) is formed between the positive x-axis and the line segment connecting the origin to point \( P \), with \( t \) shown as a blue angle in standard position. The coordinates \((1,0)\) are indicated on the positive x-axis.

### Trigonometric Functions on the Unit Circle A point \( P(x, y) \) is shown on the unit circle corresponding to a real number \( t \). Find the values of the trigonometric functions at \( t \). The point \( P \) is \( \left(\frac{15}{17}, \frac{8}{17}\right) \). **Questions:** a. \( \sin t = \) [Type an integer or a simplified fraction.] b. \( \cos t = \) [Type an integer or a simplified fraction.] c. \( \tan t = \) [Type an integer or a simplified fraction.] d. \( \csc t = \) [Type an integer or a simplified fraction.] e. \( \sec t = \) [Type an integer or a simplified fraction.] f. \( \cot t = \) [Type an integer or a simplified fraction.] **Diagram Description:** The diagram depicts a unit circle centered at the origin \((0,0)\) on the coordinate plane. The circle is highlighted with a radius reaching point \( P \) on the circle's circumference. The angle \( t \) is formed between the positive x-axis and the line segment connecting the origin to point \( P \), with \( t \) shown as a blue angle in standard position. The coordinates \((1,0)\) are indicated on the positive x-axis.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Trigonometric Functions on the Unit Circle A point \( P(x, y) \) is shown on the unit circle corresponding to a real number \( t \). Find the values of the trigonometric functions at \( t \). The point \( P \) is \( \left(\frac{15}{17}, \frac{8}{17}\right) \). **Questions:** a. \( \sin t = \) [Type an integer or a simplified fraction.] b. \( \cos t = \) [Type an integer or a simplified fraction.] c. \( \tan t = \) [Type an integer or a simplified fraction.] d. \( \csc t = \) [Type an integer or a simplified fraction.] e. \( \sec t = \) [Type an integer or a simplified fraction.] f. \( \cot t = \) [Type an integer or a simplified fraction.] **Diagram Description:** The diagram depicts a unit circle centered at the origin \((0,0)\) on the coordinate plane. The circle is highlighted with a radius reaching point \( P \) on the circle's circumference. The angle \( t \) is formed between the positive x-axis and the line segment connecting the origin to point \( P \), with \( t \) shown as a blue angle in standard position. The coordinates \((1,0)\) are indicated on the positive x-axis.
Transcribed Image Text:### Trigonometric Functions on the Unit Circle A point \( P(x, y) \) is shown on the unit circle corresponding to a real number \( t \). Find the values of the trigonometric functions at \( t \). The point \( P \) is \( \left(\frac{15}{17}, \frac{8}{17}\right) \). **Questions:** a. \( \sin t = \) [Type an integer or a simplified fraction.] b. \( \cos t = \) [Type an integer or a simplified fraction.] c. \( \tan t = \) [Type an integer or a simplified fraction.] d. \( \csc t = \) [Type an integer or a simplified fraction.] e. \( \sec t = \) [Type an integer or a simplified fraction.] f. \( \cot t = \) [Type an integer or a simplified fraction.] **Diagram Description:** The diagram depicts a unit circle centered at the origin \((0,0)\) on the coordinate plane. The circle is highlighted with a radius reaching point \( P \) on the circle's circumference. The angle \( t \) is formed between the positive x-axis and the line segment connecting the origin to point \( P \), with \( t \) shown as a blue angle in standard position. The coordinates \((1,0)\) are indicated on the positive x-axis.
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