Consider the angle shown below that has a radian measure of 0. A circle with a radius of 2.7 cm is centered at the angle's vertex, and the terminal point is shown. 1.68 Cm 2.1 cm 2.7 cm a. The terminal point's horizontal distance to the right of the center of the circle is times as large as the radius of the circle, and therefore: cos(0) Preview b. The terminal point's vertical distance above the center of the circle is times as large as the radius of the circle, and therefore: sin(8) = Preview

Calculus: Early Transcendentals
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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The image illustrates an angle with a radian measure of θ, centered at the vertex of a circle with a radius of 2.7 cm. The diagram shows the circle and the terminal side of the angle ending at a point on the circle.

**Diagram Details:**

- The circle is drawn with a blue outline and has a radius of 2.7 cm.
- The angle is positioned such that it intersects the positive x-axis.
- A right triangle is formed with the circle's radius, the x-axis, and a vertical line (from the x-axis to the terminal point of the angle).
- Measurements provided:
  - The horizontal leg (adjacent to angle θ) measures 1.68 cm.
  - The vertical leg (opposite angle θ) measures 2.11 cm.
  - The hypotenuse of the triangle, which is the radius of the circle, measures 2.7 cm.

**Problem Statement:**

1. **Horizontal Distance Analysis:**
   - The terminal point's horizontal distance to the right of the center of the circle is compared to the circle's radius.
   - Formula: \(\cos(\theta) = \frac{\text{horizontal distance}}{\text{radius}}\)

2. **Vertical Distance Analysis:**
   - The terminal point's vertical distance above the center of the circle is compared to the circle's radius.
   - Formula: \(\sin(\theta) = \frac{\text{vertical distance}}{\text{radius}}\)

**Interactive Components:**

- Text boxes are provided to calculate and enter the values of \(\cos(\theta)\) and \(\sin(\theta)\).
- A "Preview" button likely allows users to check their answers.

These activities help in understanding how the trigonometric functions cosine and sine relate to a circle's geometry and facilitate practical application of the unit circle concept.
Transcribed Image Text:The image illustrates an angle with a radian measure of θ, centered at the vertex of a circle with a radius of 2.7 cm. The diagram shows the circle and the terminal side of the angle ending at a point on the circle. **Diagram Details:** - The circle is drawn with a blue outline and has a radius of 2.7 cm. - The angle is positioned such that it intersects the positive x-axis. - A right triangle is formed with the circle's radius, the x-axis, and a vertical line (from the x-axis to the terminal point of the angle). - Measurements provided: - The horizontal leg (adjacent to angle θ) measures 1.68 cm. - The vertical leg (opposite angle θ) measures 2.11 cm. - The hypotenuse of the triangle, which is the radius of the circle, measures 2.7 cm. **Problem Statement:** 1. **Horizontal Distance Analysis:** - The terminal point's horizontal distance to the right of the center of the circle is compared to the circle's radius. - Formula: \(\cos(\theta) = \frac{\text{horizontal distance}}{\text{radius}}\) 2. **Vertical Distance Analysis:** - The terminal point's vertical distance above the center of the circle is compared to the circle's radius. - Formula: \(\sin(\theta) = \frac{\text{vertical distance}}{\text{radius}}\) **Interactive Components:** - Text boxes are provided to calculate and enter the values of \(\cos(\theta)\) and \(\sin(\theta)\). - A "Preview" button likely allows users to check their answers. These activities help in understanding how the trigonometric functions cosine and sine relate to a circle's geometry and facilitate practical application of the unit circle concept.
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