{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

pre-calc 4.5 notes - Section 4.5 Graphs of Sine and Cosine...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Section 4.5 Graphs of Sine and Cosine Functions In this section, we look at the graphs of sine and cosine functions. We use the traditional symbol x , rather than θ or t , to represent the independent variable. We use the symbol y for the dependent variable, or the function’s value at x . So we are looking at graphs of y = sin x and y = cos x in the rectangular coordinate system. In all graphs of trigonometric functions, the independent variable, x , is measured in radians. The Graph of y = sin x Graph y = sin x by listing some points on the graph. Since the period of sine is 2π, graph the function on [0, 2π] and the rest of the graph is made up of repetitions of this portion. x 0 6 π 3 π 2 π 3 2 π 6 5 π π 6 7 π 3 4 π 2 3 π 3 5 π 6 11 π y = sin x 0 2 1 2 3 1 2 3 2 1 0 2 1 - 2 3 - -1 2 3 - 2 1 - 0 You can get a more complete graph of y = sin x by continuing the portion shown above to the left and to the right. Properties of the sine function The domain is (-∞, ∞), the set of all real numbers. The range is [-1, 1], the set of all real numbers between -1 and 1, inclusive. The period is 2π. (The graph’s pattern repeats in every interval of length 2π.) The function is an odd function: sin(- x ) = - sin x Graphing Variations of y = sin x It is helpful to find x-intercepts, maximum points, and minimum points to graph these variations. The x- coordinates of the key points are x 1 = value of x where the cycle begins, x 2 = x 1 + 4 period , x 3 = x 2 + 4 period , x 4 = x
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
Image of page 2
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