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Find cos . (8, 6) r cos o 6 =

Find cos . (8, 6) r cos o 6 =

Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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**Find cos φ.** The image presents a two-dimensional coordinate system with an angle φ formed by the x-axis and a vector. The vector is indicated by an arrow leading to the point (8, 6) in the plane. ### Explanation of Diagram - The horizontal line represents the x-axis. - The vertical line represents the y-axis. - The angle φ is between the x-axis and the vector (r). - The coordinates of the endpoint of the vector are given as (8, 6). - The cosine of angle φ, denoted as cos φ, needs to be calculated. ### Task Calculate cos φ using the coordinates provided, and express your answer in the lowest terms. **Note:** The cosine of angle φ is typically calculated by using the formula cos φ = adjacent side/hypotenuse in a right triangle. Given the point coordinates (8, 6), you can find: - The adjacent side as the horizontal distance (x-coordinate = 8). - The opposite side as the vertical distance (y-coordinate = 6). - The hypotenuse (r) using the Pythagorean theorem: \( r = \sqrt{8^2 + 6^2} \). **Instruction:** 1. Compute hypotenuse: \( r = \sqrt{64 + 36} = \sqrt{100} = 10 \). 2. Calculate cos φ: \( \text{cos } φ = \frac{8}{10} = \frac{4}{5} \). Enter your answer in the provided input box.
Transcribed Image Text:**Find cos φ.** The image presents a two-dimensional coordinate system with an angle φ formed by the x-axis and a vector. The vector is indicated by an arrow leading to the point (8, 6) in the plane. ### Explanation of Diagram - The horizontal line represents the x-axis. - The vertical line represents the y-axis. - The angle φ is between the x-axis and the vector (r). - The coordinates of the endpoint of the vector are given as (8, 6). - The cosine of angle φ, denoted as cos φ, needs to be calculated. ### Task Calculate cos φ using the coordinates provided, and express your answer in the lowest terms. **Note:** The cosine of angle φ is typically calculated by using the formula cos φ = adjacent side/hypotenuse in a right triangle. Given the point coordinates (8, 6), you can find: - The adjacent side as the horizontal distance (x-coordinate = 8). - The opposite side as the vertical distance (y-coordinate = 6). - The hypotenuse (r) using the Pythagorean theorem: \( r = \sqrt{8^2 + 6^2} \). **Instruction:** 1. Compute hypotenuse: \( r = \sqrt{64 + 36} = \sqrt{100} = 10 \). 2. Calculate cos φ: \( \text{cos } φ = \frac{8}{10} = \frac{4}{5} \). Enter your answer in the provided input box.
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