+H 1 Find cos 0. (8.15) 0 ? Enter
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter1: The Six Trigonometric Functions
Section1.2: The Rectangular Coordinate System
Problem 92PS: Draw an angle in standard position whose terminal side contains the point (2, –3). Find the...
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![## Finding the Cosine of an Angle θ
To determine the cosine of an angle \(\theta\), otherwise noted as \(\cos \theta\), follow the guidance provided in the image. The image shows a graph with a marked point at (8, 15).
### Graph Explanation:
The graph includes the following elements:
- A Cartesian coordinate system with horizontal (x-axis) and vertical (y-axis) lines.
- A point marked at the coordinates \((8, 15)\).
- A right triangle formed with one vertex at the origin \((0, 0)\), the point \((8, 15)\), and another point on the x-axis.
- The angle \(\theta\) is located at the origin of the triangle, created between the x-axis and the hypotenuse of the triangle extending to the point \((8, 15)\).
### Step-by-Step Solution:
1. **Identify the Triangle Sides:**
- The adjacent side (\(x\)) to angle \(\theta\) is along the x-axis: \(8\).
- The opposite side (\(y\)) to angle \(\theta\) is along the y-axis: \(15\).
- The hypotenuse (\(r\)) can be calculated using the Pythagorean theorem:
\[
r = \sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17
\]
2. **Calculate Cosine:**
The cosine of an angle \(\theta\) in a right triangle is defined as the ratio of the length of the adjacent side to the hypotenuse.
\[
\cos \theta = \frac{\text{Adjacent Side}}{\text{Hypotenuse}} = \frac{8}{17}
\]
### Interactive Section:
- There is an input box where users can enter their answer to the question "Find \(\cos \theta\)."
- Below the input box is a button labeled "Enter" for submitting the response.
By following the above steps, you can determine that \(\cos \theta = \frac{8}{17}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88948349-7a3a-42b1-b43e-0f6310456bad%2Fb7647acd-de7a-43d5-b924-3cd29e893364%2Fg8zst5y_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Finding the Cosine of an Angle θ
To determine the cosine of an angle \(\theta\), otherwise noted as \(\cos \theta\), follow the guidance provided in the image. The image shows a graph with a marked point at (8, 15).
### Graph Explanation:
The graph includes the following elements:
- A Cartesian coordinate system with horizontal (x-axis) and vertical (y-axis) lines.
- A point marked at the coordinates \((8, 15)\).
- A right triangle formed with one vertex at the origin \((0, 0)\), the point \((8, 15)\), and another point on the x-axis.
- The angle \(\theta\) is located at the origin of the triangle, created between the x-axis and the hypotenuse of the triangle extending to the point \((8, 15)\).
### Step-by-Step Solution:
1. **Identify the Triangle Sides:**
- The adjacent side (\(x\)) to angle \(\theta\) is along the x-axis: \(8\).
- The opposite side (\(y\)) to angle \(\theta\) is along the y-axis: \(15\).
- The hypotenuse (\(r\)) can be calculated using the Pythagorean theorem:
\[
r = \sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17
\]
2. **Calculate Cosine:**
The cosine of an angle \(\theta\) in a right triangle is defined as the ratio of the length of the adjacent side to the hypotenuse.
\[
\cos \theta = \frac{\text{Adjacent Side}}{\text{Hypotenuse}} = \frac{8}{17}
\]
### Interactive Section:
- There is an input box where users can enter their answer to the question "Find \(\cos \theta\)."
- Below the input box is a button labeled "Enter" for submitting the response.
By following the above steps, you can determine that \(\cos \theta = \frac{8}{17}\).
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