Table of contents
- 0. Review of College Algebra4h 43m
- 1. Measuring Angles39m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
4. Graphing Trigonometric Functions
Graphs of Tangent and Cotangent Functions
Problem 4.17b
Textbook Question
Textbook QuestionGraph each function over a one-period interval.
y = 2 tan (¼ x)
Verified Solution
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
0m:0sPlay a video:
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Period of a Trigonometric Function
The period of a trigonometric function is the length of one complete cycle of the function. For the tangent function, the standard period is π. However, when the function is modified, such as in y = 2 tan(¼ x), the period changes based on the coefficient of x. In this case, the period becomes 4π, as it is calculated by dividing the standard period by the coefficient of x.
Recommended video:
5:33
Period of Sine and Cosine Functions
Transformation of Functions
Transformations of functions involve shifting, stretching, or compressing the graph of a function. In the function y = 2 tan(¼ x), the '2' indicates a vertical stretch, meaning the output values of the tangent function are multiplied by 2, making the graph steeper. The '¼' indicates a horizontal stretch, which affects the period of the function, resulting in a wider graph.
Recommended video:
4:22
Domain and Range of Function Transformations
Graphing the Tangent Function
The tangent function has unique characteristics, including vertical asymptotes where the function is undefined, occurring at odd multiples of π/2. When graphing y = 2 tan(¼ x), it is essential to identify these asymptotes and the points where the function crosses the x-axis. The graph will repeat every 4π, and understanding the behavior of the tangent function helps in accurately plotting its graph over the specified interval.
Recommended video:
5:43
Introduction to Tangent Graph
Watch next
Master Introduction to Tangent Graph with a bite sized video explanation from Nick Kaneko
Start learningRelated Videos
Related Practice