Consider the following unit Circle -By the definition of the sine function, sin(Ø)= x, -x, y, or -y? -The y coordinate of the point on the unit circle that intersects the terminal ray of π-Ø is: x, -x, y, -y? -Therefore, sin (π - Ø )= sin, -sin, cos, or -cos? -This means that the sine function is symmetric about the: x-axis, y-axis, or origin?
Consider the following unit Circle -By the definition of the sine function, sin(Ø)= x, -x, y, or -y? -The y coordinate of the point on the unit circle that intersects the terminal ray of π-Ø is: x, -x, y, -y? -Therefore, sin (π - Ø )= sin, -sin, cos, or -cos? -This means that the sine function is symmetric about the: x-axis, y-axis, or origin?
Calculus: Early Transcendentals
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Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
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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Consider the following unit Circle
-By the definition of the sine function, sin(Ø)= x, -x, y, or -y?
-The y coordinate of the point on the unit circle that intersects the terminal ray of π-Ø is: x, -x, y, -y?
-Therefore, sin (π - Ø )= sin, -sin, cos, or -cos?
-This means that the sine function is symmetric about the: x-axis, y-axis, or origin?
Transcribed Image Text:The image depicts a unit circle graph on a Cartesian coordinate plane with angles and coordinates marked. Here is a detailed description:
1. **Axes and Circle:**
- A unit circle is centered at the origin (0,0) with a radius of 1.
- The x-axis ranges from -1 to 1, and the y-axis also ranges from -1 to 1.
2. **Labeled Points:**
- The point \((x, y)\) is marked in the first quadrant on the circle.
- The point \((-x, y)\) is marked in the second quadrant on the circle.
3. **Angles:**
- The angle \(\theta\) is marked at the origin with a red arc, indicating the angle between the positive x-axis and the line segment from the origin to \((x, y)\).
- The angle \(\pi - \theta\) is marked with a blue arc, indicating the angle between the positive x-axis and the line segment from the origin to \((-x, y)\).
4. **Coordinates:**
- The graph shows symmetry along the vertical axis, illustrating that the x-coordinate changes sign from right to left while the y-coordinate remains the same.
This diagram is commonly used to explain angle and coordinate relationships in trigonometry, particularly in the context of symmetry and transformations on the unit circle.
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