Graph each function using radians. Be sure to graph your asymptotes and name period, domain, and range. 1. y=tan(40) 2. y = tan (0-7)

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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**Graph Each Function Using Radians**

Instructions: Be sure to graph your asymptotes and name the period, domain, and range for each function.

1. **\( y = \tan(4\theta) \)**
   - [Graph not shown; plot tan function with horizontal stretch]
   
2. **\( y = \tan \left( \theta - \frac{\pi}{4} \right) \)**
   - [Graph not shown; plot tan function with horizontal shift]

3. **\( y = 2\tan(\theta) \)**
   - [Graph not shown; plot tan function with vertical stretch]

4. **\( y = -2\tan \left( \theta - \frac{\pi}{4} \right) \)**
   - [Graph not shown; plot tan function with vertical stretch and reflection, shift]

5. **\( y = \frac{1}{4} \tan(\theta) + 1 \)**
   - [Graph not shown; plot tan function with vertical compression and upward shift]

6. **\( y = -\tan(3\theta) - 1 \)**
   - [Graph not shown; plot tan function with vertical reflection, horizontal compression, and downward shift]

For each graph:
- **Asymptotes**: Draw asymptotes for undefined points of the tangent function.
- **Period**: Specify the horizontal length for one complete cycle of the function.
- **Domain**: Describe the set of all possible input values (angles) for the function.
- **Range**: Determine the set of all possible output values for the function. 

Please use graphing tools to visualize each function according to its transformations.
Transcribed Image Text:**Graph Each Function Using Radians** Instructions: Be sure to graph your asymptotes and name the period, domain, and range for each function. 1. **\( y = \tan(4\theta) \)** - [Graph not shown; plot tan function with horizontal stretch] 2. **\( y = \tan \left( \theta - \frac{\pi}{4} \right) \)** - [Graph not shown; plot tan function with horizontal shift] 3. **\( y = 2\tan(\theta) \)** - [Graph not shown; plot tan function with vertical stretch] 4. **\( y = -2\tan \left( \theta - \frac{\pi}{4} \right) \)** - [Graph not shown; plot tan function with vertical stretch and reflection, shift] 5. **\( y = \frac{1}{4} \tan(\theta) + 1 \)** - [Graph not shown; plot tan function with vertical compression and upward shift] 6. **\( y = -\tan(3\theta) - 1 \)** - [Graph not shown; plot tan function with vertical reflection, horizontal compression, and downward shift] For each graph: - **Asymptotes**: Draw asymptotes for undefined points of the tangent function. - **Period**: Specify the horizontal length for one complete cycle of the function. - **Domain**: Describe the set of all possible input values (angles) for the function. - **Range**: Determine the set of all possible output values for the function. Please use graphing tools to visualize each function according to its transformations.
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