ADJ B Again, find the length of the red side of the triangle (labeled ADJ), and use that to fi coordinate of the blue point. Enter exact expressions or round your answers to the thousandth.
ADJ B Again, find the length of the red side of the triangle (labeled ADJ), and use that to fi coordinate of the blue point. Enter exact expressions or round your answers to the thousandth.
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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Question
![### Part 2:
The circle below is still centered at the origin and has a radius of length 1. The measure of angle \( B \) is 0.94 radians.
#### Diagram Description:
- A circle with a radius of 1 unit centered at the origin (0,0).
- A right triangle is inscribed in the circle.
- The hypotenuse of the triangle is a radius of the circle, with one endpoint at the origin and the other on the circumference.
- The angle \( B \) at the origin is marked as 0.94 radians.
- The adjacent side (labeled ADJ) is drawn from the origin along the horizontal axis to the vertical leg of the triangle.
#### Instructions:
Again, find the length of the red side of the triangle (labeled ADJ), and use that to find the \( x \) coordinate of the blue point. Enter exact expressions or round your answers to the nearest thousandth.
#### Input Fields:
* Length of red side = [Input Box]
* \( x \) coordinate of blue point = [Input Box]
---
### Solution Steps:
1. **Calculate the Length of the Red Side (ADJ):**
Use the trigonometric relationship for cosine in a right triangle:
\[
\cos(B) = \text{adjacent} / \text{hypotenuse}
\]
Given:
\[
\cos(0.94) = \text{ADJ} / 1
\]
Therefore:
\[
\text{ADJ} = \cos(0.94)
\]
Calculate \(\cos(0.94)\) using a calculator.
2. **Determine the \( x \) Coordinate of the Blue Point:**
The \( x \) coordinate of the blue point is the same as the length of ADJ because it lies along the \( x \)-axis.
---
### Example Calculation:
1. Evaluate \(\text{ADJ}\):
\[
\text{ADJ} = \cos(0.94) \approx 0.5878 \text{ (rounded to nearest thousandth)}
\]
2. The \( x \) coordinate of the blue point is therefore:
\[
\text{ADJ} = 0.588 \text{ (rounded to nearest thousandth)}
\]
### Input Fields Example](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F89e7fbf9-0e55-4f4a-a0db-4898252833e3%2F080c9857-8574-40a6-abc3-f70ef8e9f351%2F19i9oqi_processed.png&w=3840&q=75)
Transcribed Image Text:### Part 2:
The circle below is still centered at the origin and has a radius of length 1. The measure of angle \( B \) is 0.94 radians.
#### Diagram Description:
- A circle with a radius of 1 unit centered at the origin (0,0).
- A right triangle is inscribed in the circle.
- The hypotenuse of the triangle is a radius of the circle, with one endpoint at the origin and the other on the circumference.
- The angle \( B \) at the origin is marked as 0.94 radians.
- The adjacent side (labeled ADJ) is drawn from the origin along the horizontal axis to the vertical leg of the triangle.
#### Instructions:
Again, find the length of the red side of the triangle (labeled ADJ), and use that to find the \( x \) coordinate of the blue point. Enter exact expressions or round your answers to the nearest thousandth.
#### Input Fields:
* Length of red side = [Input Box]
* \( x \) coordinate of blue point = [Input Box]
---
### Solution Steps:
1. **Calculate the Length of the Red Side (ADJ):**
Use the trigonometric relationship for cosine in a right triangle:
\[
\cos(B) = \text{adjacent} / \text{hypotenuse}
\]
Given:
\[
\cos(0.94) = \text{ADJ} / 1
\]
Therefore:
\[
\text{ADJ} = \cos(0.94)
\]
Calculate \(\cos(0.94)\) using a calculator.
2. **Determine the \( x \) Coordinate of the Blue Point:**
The \( x \) coordinate of the blue point is the same as the length of ADJ because it lies along the \( x \)-axis.
---
### Example Calculation:
1. Evaluate \(\text{ADJ}\):
\[
\text{ADJ} = \cos(0.94) \approx 0.5878 \text{ (rounded to nearest thousandth)}
\]
2. The \( x \) coordinate of the blue point is therefore:
\[
\text{ADJ} = 0.588 \text{ (rounded to nearest thousandth)}
\]
### Input Fields Example
**Description of the Diagram:**
The diagram consists of a circle centered at the origin (0, 0), and a right-angled triangle is drawn within the circle. The hypotenuse of the triangle lies along the radius of the circle and has a length of \( 1 \). The right angle is between the two legs of the triangle, one of which is horizontal and the other which is vertical. The angle \( A \) at the circle's origin is \( 0.68 \) radians. The horizontal leg is labeled "ADJ" in red, and we are to determine its length.
**Tasks:**
Find the length of the red side of the triangle (labeled ADJ), and use that to find the \( x \) coordinate of the blue point. Enter exact expressions or round your answers to the nearest thousandth.
### Steps:
1. **Calculate the length of the red side (ADJ):**
- Since the hypotenuse is \( 1 \) and given that angle \( A \) is \( 0.68 \) radians, we can use the cosine function.
- \( \cos(A) = \frac{\text{adjacent}}{\text{hypotenuse}} \)
- Therefore, \( \cos(0.68) = \frac{\text{ADJ}}{1} \)
- \( \text{ADJ} = \cos(0.68) \)
2. **Find the \( x \) coordinate of the blue point:**
- The \( x \) coordinate of the blue point is the length of the adjacent (ADJ) side calculated above.
- Therefore, \( x = \cos(0.68) \)
### Formulas:
- \( \cos(A) = \frac{\text{adjacent}}{\text{hypotenuse}} \)
### Answers:
- Length of red side = \( \cos(0.68) \approx 0.776 \)
- \( x \) coordinate of blue point = \( 0.776 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F89e7fbf9-0e55-4f4a-a0db-4898252833e3%2F080c9857-8574-40a6-abc3-f70ef8e9f351%2F17nugin_processed.png&w=3840&q=75)
Transcribed Image Text:### Part 1:
The circle below is centered at the origin and has a radius of length \( 1 \) (so that the hypotenuse of the triangle shown has length \( 1 \)). The measure of angle \( A \) is \( 0.68 \) radians.
**Description of the Diagram:**
The diagram consists of a circle centered at the origin (0, 0), and a right-angled triangle is drawn within the circle. The hypotenuse of the triangle lies along the radius of the circle and has a length of \( 1 \). The right angle is between the two legs of the triangle, one of which is horizontal and the other which is vertical. The angle \( A \) at the circle's origin is \( 0.68 \) radians. The horizontal leg is labeled "ADJ" in red, and we are to determine its length.
**Tasks:**
Find the length of the red side of the triangle (labeled ADJ), and use that to find the \( x \) coordinate of the blue point. Enter exact expressions or round your answers to the nearest thousandth.
### Steps:
1. **Calculate the length of the red side (ADJ):**
- Since the hypotenuse is \( 1 \) and given that angle \( A \) is \( 0.68 \) radians, we can use the cosine function.
- \( \cos(A) = \frac{\text{adjacent}}{\text{hypotenuse}} \)
- Therefore, \( \cos(0.68) = \frac{\text{ADJ}}{1} \)
- \( \text{ADJ} = \cos(0.68) \)
2. **Find the \( x \) coordinate of the blue point:**
- The \( x \) coordinate of the blue point is the length of the adjacent (ADJ) side calculated above.
- Therefore, \( x = \cos(0.68) \)
### Formulas:
- \( \cos(A) = \frac{\text{adjacent}}{\text{hypotenuse}} \)
### Answers:
- Length of red side = \( \cos(0.68) \approx 0.776 \)
- \( x \) coordinate of blue point = \( 0.776 \)
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