Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
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...
Related questions
Question

Transcribed Image Text:**Determining the Ordered Pair on the Unit Circle for -45° Angle**
To find the corresponding ordered pair for the point on the unit circle at an angle of -45°, we rely on the knowledge of trigonometric functions on the unit circle.
1. **Understanding the Unit Circle**:
- The unit circle is a circle with a radius of 1 centered at the origin (0,0) of a coordinate plane.
- Points on the unit circle are represented as (cos(θ), sin(θ)) where θ is the angle in standard position.
2. **Angle of -45°**:
- Angles in standard position are measured from the positive x-axis. A negative angle indicates the direction of measurement is clockwise.
- Thus, an angle of -45° indicates moving 45° clockwise from the positive x-axis.
3. **Coordinates at -45°**:
- The coordinates of the unit circle at -45° are derived from the corresponding values of cosine and sine.
- For -45°, both cosine and sine values are \(\frac{\sqrt{2}}{2}\), but since it’s measured in the clockwise direction, the sine value will be negative.
**Possible Answers:**
The given options are:
```
O ( √2/2 , √2/2 )
O ( -√2/2 , √2/2 )
O ( √2/2 , -√2/2 )
O ( -√2/2 , -√2/2 )
```
The correct order pair is:
O ( √2/2 , -√2/2 )
Thus, a point on the unit circle corresponding to an angle of -45° has coordinates \((\frac{√2}{2}, −\frac{√2}{2})\).
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 6 images

Recommended textbooks for you

Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning

Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON

Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON

Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning

Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON

Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON

Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman


Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning