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Determine the corresponding ordered pair of the point on the unit circle for the following angle: -45 口语) 0 (3) 0) 0 )

Determine the corresponding ordered pair of the point on the unit circle for the following angle: -45 口语) 0 (3) 0) 0 )

Calculus: Early Transcendentals
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...
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**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 \((\frac{√2}{2}, −\frac{√2}{2})\).
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 \((\frac{√2}{2}, −\frac{√2}{2})\).
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