{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Unit 4 Section 4 - 4.4 GRAPHS OF CIRCULAR FUNCTIONS Graphs...

Info icon This preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
4.4 GRAPHS OF CIRCULAR FUNCTIONS Graphs of circular functions are easier to sketch compared to the graphs of algebraic functions since they have properties that make their graphs more “predictable”. Some of these properties include period, amplitude, and phase shifts. Properties of the Graph of Circular Functions 1. Circular functions are periodic functions. This means that their function values repeat after a fixed interval. The fixed interval p is called the period (or wavelength ) . This property can be observed in their graphs. A cycle is simply the portion of a graph of a function f over an interval of length equal to the period of f. 2. The amplitude a (or maximum function value) of a graph of a periodic function refers to one- half the absolute difference between the highest and lowest function values. 3. Phase shift is a horizontal (or vertical) shift from the standard graph. Graph of the Sine and Cosine Functions The sine function defined by has the following properties: The domain is . The range is . The amplitude is equal to 1. There is no phase shift. Figure 1. The Sine Curve
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
The cosine function defined by has the following properties: The domain is . The range is . The amplitude is equal to 1. There is no phase shift. Figure 2. The Cosine Curve General Form of the Sine and Cosine Functions The general forms of the sine and cosine functions are as follows: where a, b, h and k are constants and a, b are nonzero. PROPERTIES: 1. The amplitude of the graphs of the sine and cosine functions are given by . 2. The range is also affected by the value of , that is, . 3. The period of the graph is given by the formula . 4. The horizontal phase shift is determined by the constant . If , then the graph shifts units to the right. If , then the graph shifts units to the left. 5. The vertical phase shift is determined by the constant . If , then the graph shifts units upward. If , then the graph shifts units downward.
Image of page 2
Sketching One Cycle of the Graph To sketch a cycle of the graph of the sine and cosine functions, do the following: 1. Identify values for a, b, k , and h. 2. Determine the amplitude, range, period and phase shift of the function.
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern