Express as a function of a DIFFERENT angle, os0<360. sin(191°)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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![**Transcription for Educational Website:**
---
**Trigonometric Functions: Problem Example**
**Problem Statement:**
Express the given trigonometric function as a function of a different angle, where \(0 \leq \theta < 360\).
\[ \sin(191^\circ) \]
**Interactive Solution Input:**
\[ \sin(\text{[ ]}) \]
<button>Submit Answer</button>
---
**Explanation:**
Given the angle \(191^\circ\), we need to express \( \sin(191^\circ) \) as a sine function of a different angle within the range \(0^\circ\) to \(360^\circ\).
To do this, consider the properties of the sine function and how it behaves with respect to angle transformations.
**Key Concepts:**
- Understanding sine function transformations and symmetry properties
- Knowing how to find equivalent angles using periodicity and reference angles
**Instructions:**
1. Determine if the angle can be transformed within the given range by adding or subtracting \(180^\circ\) or \(360^\circ\) if necessary.
2. Check for sine function properties such as \(\sin(\theta + 180^\circ) = -\sin(\theta)\).
3. Input the equivalent angle into the provided answer box.
**Note:**
This exercise aims to solidify your grasp of trigonometric identities and transformations.
**Hint:**
Since \( \sin \) is periodic with a period of \(360^\circ\), angles that differ by multiples of \(360^\circ\) have the same sine value, and angles related by \(180^\circ\) will have the same absolute sine value but maybe a different sign.
For example, angles in the second and third quadrants can be transformed to corresponding angles in the first quadrant for simplification.
Good luck!
---
**Interactive Component Description:**
The interactive component consists of an input field where students can type in the equivalent angle after performing the necessary trigonometric transformations. There is also a "Submit Answer" button to validate and check their response.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F49e7cf44-c454-4b76-b99a-274946cc3378%2F7a171dc3-8f7c-462c-8f53-9fb70f2d4848%2Fd6j1pap_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website:**
---
**Trigonometric Functions: Problem Example**
**Problem Statement:**
Express the given trigonometric function as a function of a different angle, where \(0 \leq \theta < 360\).
\[ \sin(191^\circ) \]
**Interactive Solution Input:**
\[ \sin(\text{[ ]}) \]
<button>Submit Answer</button>
---
**Explanation:**
Given the angle \(191^\circ\), we need to express \( \sin(191^\circ) \) as a sine function of a different angle within the range \(0^\circ\) to \(360^\circ\).
To do this, consider the properties of the sine function and how it behaves with respect to angle transformations.
**Key Concepts:**
- Understanding sine function transformations and symmetry properties
- Knowing how to find equivalent angles using periodicity and reference angles
**Instructions:**
1. Determine if the angle can be transformed within the given range by adding or subtracting \(180^\circ\) or \(360^\circ\) if necessary.
2. Check for sine function properties such as \(\sin(\theta + 180^\circ) = -\sin(\theta)\).
3. Input the equivalent angle into the provided answer box.
**Note:**
This exercise aims to solidify your grasp of trigonometric identities and transformations.
**Hint:**
Since \( \sin \) is periodic with a period of \(360^\circ\), angles that differ by multiples of \(360^\circ\) have the same sine value, and angles related by \(180^\circ\) will have the same absolute sine value but maybe a different sign.
For example, angles in the second and third quadrants can be transformed to corresponding angles in the first quadrant for simplification.
Good luck!
---
**Interactive Component Description:**
The interactive component consists of an input field where students can type in the equivalent angle after performing the necessary trigonometric transformations. There is also a "Submit Answer" button to validate and check their response.
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