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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Question
![Find the reference angle for the given angle.
(a) 175°
[ ]
(b) 340°
[ ]
(c) 730°
[ ]
### Explanation:
A reference angle is the acute angle that an angle makes with the x-axis. It is always between 0° and 90°, irrespective of the quadrant in which the angle lies. To find the reference angle:
- For angles between 0° and 360°:
- If the angle is in the first quadrant, the reference angle is the angle itself.
- If the angle is in the second quadrant, subtract the angle from 180°.
- If the angle is in the third quadrant, subtract 180° from the angle.
- If the angle is in the fourth quadrant, subtract the angle from 360°.
- For angles greater than 360° or less than 0°, find an equivalent angle between 0° and 360° by adding or subtracting 360° repeatedly, then use the above rules.
Please fill in the boxes with the correct reference angles for each given angle.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F05276323-f51a-4f52-b582-fb773aa52696%2F33ef06ad-03c0-4907-b0e3-faa3fd346b0c%2Fcc1peyo_processed.png&w=3840&q=75)
Transcribed Image Text:Find the reference angle for the given angle.
(a) 175°
[ ]
(b) 340°
[ ]
(c) 730°
[ ]
### Explanation:
A reference angle is the acute angle that an angle makes with the x-axis. It is always between 0° and 90°, irrespective of the quadrant in which the angle lies. To find the reference angle:
- For angles between 0° and 360°:
- If the angle is in the first quadrant, the reference angle is the angle itself.
- If the angle is in the second quadrant, subtract the angle from 180°.
- If the angle is in the third quadrant, subtract 180° from the angle.
- If the angle is in the fourth quadrant, subtract the angle from 360°.
- For angles greater than 360° or less than 0°, find an equivalent angle between 0° and 360° by adding or subtracting 360° repeatedly, then use the above rules.
Please fill in the boxes with the correct reference angles for each given angle.
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