3π 4 The graph below shows the angle A = A = 3π/4 Find the exact value (no rounding) for cosine. COS (³7) 4 inside the unit circle. a
3π 4 The graph below shows the angle A = A = 3π/4 Find the exact value (no rounding) for cosine. COS (³7) 4 inside the unit circle. a
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°.
Related questions
Question
In the diagram:
- The angle \( A \) is measured in radians and is equal to \( \frac{3\pi}{4} \).
- The angle is shown extending counter-clockwise from the positive x-axis.
- A right triangle is formed inside the unit circle. The hypotenuse of this right triangle is the radius of the unit circle, which is 1.
- The horizontal leg (adjacent to the angle) is drawn along the x-axis.
- The vertical leg (opposite to the angle) is drawn perpendicular to the x-axis, reaching the point where the hypotenuse intersects the circle.
#### Problem Statement
**Question:** Find the exact value (no rounding) for cosine.
\[ \cos\left(\frac{3\pi}{4}\right) = \]
*Note: The cosine function, \( \cos \theta \), gives the x-coordinate of the point on the unit circle that corresponds to the angle \( \theta \). For angle \(\theta = \frac{3\pi}{4}\), the exact cosine value can be determined as follows.*
Use the properties of the unit circle and the symmetry in the quadrants to find the exact value.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdc1123ec-a0e0-4e35-afe0-df78f47a58b5%2F55bb8b60-72e6-44f7-b555-785b4b011561%2Fv4rcf4r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Angles in the Unit Circle
#### The Angle \( A = \frac{3\pi}{4} \) Inside the Unit Circle
The diagram below illustrates the angle \( A = \frac{3\pi}{4} \) within the unit circle. A unit circle is a circle with a radius of 1, centered at the origin (0,0) on the Cartesian coordinate system.
In the diagram:
- The angle \( A \) is measured in radians and is equal to \( \frac{3\pi}{4} \).
- The angle is shown extending counter-clockwise from the positive x-axis.
- A right triangle is formed inside the unit circle. The hypotenuse of this right triangle is the radius of the unit circle, which is 1.
- The horizontal leg (adjacent to the angle) is drawn along the x-axis.
- The vertical leg (opposite to the angle) is drawn perpendicular to the x-axis, reaching the point where the hypotenuse intersects the circle.
#### Problem Statement
**Question:** Find the exact value (no rounding) for cosine.
\[ \cos\left(\frac{3\pi}{4}\right) = \]
*Note: The cosine function, \( \cos \theta \), gives the x-coordinate of the point on the unit circle that corresponds to the angle \( \theta \). For angle \(\theta = \frac{3\pi}{4}\), the exact cosine value can be determined as follows.*
Use the properties of the unit circle and the symmetry in the quadrants to find the exact value.
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