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 the Sine and Cosine Functions
5:29 minutes
Problem 4
Textbook Question
Textbook QuestionIn Exercises 1–6, determine the amplitude and period of each function. Then graph one period of the function. y = 1/2 sin π/3 x
Verified Solution
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
5mPlay a video:
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Amplitude
Amplitude refers to the maximum height of a wave from its central axis. In the context of sine functions, it is determined by the coefficient in front of the sine term. For the function y = 1/2 sin(π/3 x), the amplitude is 1/2, indicating that the wave oscillates between 1/2 and -1/2.
Recommended video:
5:05
Amplitude and Reflection of Sine and Cosine
Period
The period of a trigonometric function is the length of one complete cycle of the wave. For sine functions, the period can be calculated using the formula P = 2π / |b|, where b is the coefficient of x. In this case, with b = π/3, the period is 2π / (π/3) = 6, meaning the function completes one full cycle every 6 units along the x-axis.
Recommended video:
5:33
Period of Sine and Cosine Functions
Graphing Trigonometric Functions
Graphing trigonometric functions involves plotting the function's values over a specified interval. For y = 1/2 sin(π/3 x), one period can be graphed from x = 0 to x = 6. The graph will show a smooth wave oscillating between 1/2 and -1/2, starting at the origin, reaching its maximum at x = 3, and returning to the axis at x = 6.
Recommended video:
6:04
Introduction to Trigonometric Functions
Watch next
Master Graph of Sine and Cosine Function with a bite sized video explanation from Nick Kaneko
Start learningRelated Videos
Related Practice