The terminal side of an angle 0 in standard position passes through the point (-3,-4). Use the figure to find the following value. cos 8 cos = (Type an exact answer in simplified form. Rationalize all denominators.) G a
The terminal side of an angle 0 in standard position passes through the point (-3,-4). Use the figure to find the following value. cos 8 cos = (Type an exact answer in simplified form. Rationalize all denominators.) G 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
![**Trigonometry Practice Problem**
---
**Problem Statement:**
The terminal side of an angle θ in standard position passes through the point (-3, -4). Use the figure to find the following value.
\[ \cos \theta \]
**Figure Explanation:**
The figure accompanying the problem shows a coordinate plane with both the x-axis and y-axis labeled. An angle θ is depicted in standard position with its terminal side intersecting the point (-3, -4). The figure includes a right triangle with legs of length 3 and 4 units, corresponding to the x and y coordinates respectively. The hypotenuse is implied by the diagram and forms the side opposite to the angle θ, originating from the origin (0,0) and passing through the point (-3, -4).
**Calculation:**
Find \( \cos \theta \) using the coordinates of the point and the Pythagorean theorem.
\[ \cos \theta = \frac{\text{adjacent side}}{\text{hypotenuse}} = \frac{x}{r} \]
Where:
- \( x \) is -3 (the adjacent side, projection on the x-axis),
- \( r \) is the hypotenuse.
First, calculate the hypotenuse (\( r \)) using the Pythagorean theorem:
\[ r = \sqrt{x^2 + y^2} = \sqrt{(-3)^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \]
Then,
\[ \cos \theta = \frac{-3}{5} \]
\[ \cos \theta = -\frac{3}{5} \]
---
**Answer Box:**
\[ \cos \theta = -\frac{3}{5} \]
(Type an exact answer in simplified form. Rationalize all denominators.)
---
This trigonometric problem helps to understand how to determine the cosine of an angle given its coordinates in a standard position on the coordinate plane. By using the figure and the relationships in a right triangle, students apply the Pythagorean theorem and trigonometric definitions to find the exact value.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9c3214b5-f2f5-4a89-904a-2906edf42c76%2F868cf7c7-62c5-4e87-817c-e3538d460352%2Fjrehu9e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Trigonometry Practice Problem**
---
**Problem Statement:**
The terminal side of an angle θ in standard position passes through the point (-3, -4). Use the figure to find the following value.
\[ \cos \theta \]
**Figure Explanation:**
The figure accompanying the problem shows a coordinate plane with both the x-axis and y-axis labeled. An angle θ is depicted in standard position with its terminal side intersecting the point (-3, -4). The figure includes a right triangle with legs of length 3 and 4 units, corresponding to the x and y coordinates respectively. The hypotenuse is implied by the diagram and forms the side opposite to the angle θ, originating from the origin (0,0) and passing through the point (-3, -4).
**Calculation:**
Find \( \cos \theta \) using the coordinates of the point and the Pythagorean theorem.
\[ \cos \theta = \frac{\text{adjacent side}}{\text{hypotenuse}} = \frac{x}{r} \]
Where:
- \( x \) is -3 (the adjacent side, projection on the x-axis),
- \( r \) is the hypotenuse.
First, calculate the hypotenuse (\( r \)) using the Pythagorean theorem:
\[ r = \sqrt{x^2 + y^2} = \sqrt{(-3)^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \]
Then,
\[ \cos \theta = \frac{-3}{5} \]
\[ \cos \theta = -\frac{3}{5} \]
---
**Answer Box:**
\[ \cos \theta = -\frac{3}{5} \]
(Type an exact answer in simplified form. Rationalize all denominators.)
---
This trigonometric problem helps to understand how to determine the cosine of an angle given its coordinates in a standard position on the coordinate plane. By using the figure and the relationships in a right triangle, students apply the Pythagorean theorem and trigonometric definitions to find the exact value.
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