Find the reference angle for the given angle. (a) 175° (b) 340° (c) 730°

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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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.
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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