Consider the angle shown below with an initial ray pointing in the 3-o'clock direction that measures θθ radians (where 0≤θ<2π0≤θ<2π). The circle's radius is 2.6 units long and the terminal point is (−0.59,2.53)(-0.59,2.53).
Consider the angle shown below with an initial ray pointing in the 3-o'clock direction that measures θθ radians (where 0≤θ<2π0≤θ<2π). The circle's radius is 2.6 units long and the terminal point is (−0.59,2.53)(-0.59,2.53).
Consider the angle shown below with an initial ray pointing in the 3-o'clock direction that measures θθ radians (where 0≤θ<2π0≤θ<2π). The circle's radius is 2.6 units long and the terminal point is (−0.59,2.53)(-0.59,2.53).
Consider the angle shown below with an initial ray pointing in the 3-o'clock direction that measures θθ radians (where 0≤θ<2π0≤θ<2π). The circle's radius is 2.6 units long and the terminal point is (−0.59,2.53)(-0.59,2.53).
Transcribed Image Text:### Trigonometry and Angles
In this activity, we will calculate the slope of a terminal ray, determine its angle, and verify the accuracy of our results.
#### Diagram Explanation
The diagram presented is a coordinate plane grid with a circle centered at the origin and radius 3. The x and y axes are labeled, with markings from -3 to 3. A terminal ray extends from the origin to the point (-0.59, 2.53) on the grid, crossing the circle's boundary. The slope \( m \) of this terminal ray, as well as the angle \( \theta \) it forms with the positive x-axis, will be determined through the following steps:
#### Detailed Steps and Calculations
1. **Determine the slope of the terminal ray:**
- The coordinates of the point on the terminal ray are given as (-0.59, 2.53).
- Slope \( m \) is calculated using the rise over run formula:
\[
m = \frac{2.53 - 0}{-0.59 - 0} = \frac{2.53}{-0.59}
\]
- Substituting the values:
\[
m = \frac{2.53}{-0.59} = -4.288135593220339
\]
2. **Calculate the arctangent to find the angle \( \theta \)**
- Use the arctangent function to determine the angle:
\[
\theta = \tan^{-1}(m) = \tan^{-1}(-4.288135593220339)
\]
3. **Verify if the angle \( \theta \) obtained is correct**
- Typically, an answer of "Yes" is expected if the value adheres to the expected range for angle \( \theta \).
4. **Determine the exact value of \( \theta \)**
- Use a calculator to find the arctangent:
\[
\theta = \arctan(-4.288135593220339)
\]
Make sure to utilize a reliable calculator for precise values and convert the angles to degrees if necessary.
#### Submission
After performing the steps above, please enter your calculated values in the corresponding fields and verify your answers before submitting your results.
---
Click "Submit" once you have completed all fields.
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Two-dimensional figure measured in terms of radius. It is formed by a set of points that are at a constant or fixed distance from a fixed point in the center of the plane. The parts of the circle are circumference, radius, diameter, chord, tangent, secant, arc of a circle, and segment in a circle.
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![### Trigonometry and Angles
In this activity, we will calculate the slope of a terminal ray, determine its angle, and verify the accuracy of our results.
#### Diagram Explanation
The diagram presented is a coordinate plane grid with a circle centered at the origin and radius 3. The x and y axes are labeled, with markings from -3 to 3. A terminal ray extends from the origin to the point (-0.59, 2.53) on the grid, crossing the circle's boundary. The slope \( m \) of this terminal ray, as well as the angle \( \theta \) it forms with the positive x-axis, will be determined through the following steps:
#### Detailed Steps and Calculations
1. **Determine the slope of the terminal ray:**
- The coordinates of the point on the terminal ray are given as (-0.59, 2.53).
- Slope \( m \) is calculated using the rise over run formula:
\[
m = \frac{2.53 - 0}{-0.59 - 0} = \frac{2.53}{-0.59}
\]
- Substituting the values:
\[
m = \frac{2.53}{-0.59} = -4.288135593220339
\]
2. **Calculate the arctangent to find the angle \( \theta \)**
- Use the arctangent function to determine the angle:
\[
\theta = \tan^{-1}(m) = \tan^{-1}(-4.288135593220339)
\]
3. **Verify if the angle \( \theta \) obtained is correct**
- Typically, an answer of "Yes" is expected if the value adheres to the expected range for angle \( \theta \).
4. **Determine the exact value of \( \theta \)**
- Use a calculator to find the arctangent:
\[
\theta = \arctan(-4.288135593220339)
\]
Make sure to utilize a reliable calculator for precise values and convert the angles to degrees if necessary.
#### Submission
After performing the steps above, please enter your calculated values in the corresponding fields and verify your answers before submitting your results.
---
Click "Submit" once you have completed all fields.
[Submit Button]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F17081990-d618-4b49-b16b-b1ec50dc9574%2F076dfce8-420b-4bc8-a0c3-7635c1c30122%2Ffotn7a_processed.png&w=3840&q=75)
