Transformations Of Sine And Cosine Math

Transformations of the sine and cosine graph an exploration by sharon k.

Transformations of sine and cosine math. Locate start of cyclephase shift locate start of cycle. If a and b are 1 both graphs have an amplitude of 1 and a period of 2π. Sine and cosine positive and negative geogebra materials. 8 vertical reflection if 0 123456 7 horizontal stretch or compression by a factor of 9.

Use the applet to view the four basic shapes. L3 transformations of sine and cosine part 1 equation à graph mcr3u jensen section 1. The function sin x is odd so its graph is symmetric about the origin. Write the equation of the sinusoidal function given the graph.

The function cos x is even so its graph is symmetric about the y axis. Graphing trigonometric functions analyzing the amplitude and periods of the sine and cosine functions. The video narrative specifically explains this lesson s warm up transformations of sine and cosine which asks students to determine which of two students is correct in finding the period of a cosine function. The domain for the sine and cosine functions are all real numbers or the range of the graph in the figure has been stretched because of the amplitude change and shifted down.

When identifying a sinusoidal function you may use the basic shape of either the sine curve or the cosine curve one is just a horizontal transformation of the other. O kelley this is an exploration for advanced algebra or precalculus teachers who have introduced their students to the basic sine and cosine graphs and now want their students to explore how changes to the equations affect the graphs. Review of sine and cosine functions sin or cos vertical stretch or compression by a factor of. Maximum value minimum value sinusoidal axis amplitude period b phase shift sine function cosine function.

The curve in the figure above can take the equation or. Math worksheets examples videos worksheets solutions and activities to help algebra 2 students learn how sine and cosine graphs are transformed. The basic sine and cosine functions have a period of 2 pi. Use the formula 2π b to find the period.

When b is greater than 1 the period decreases. To find the range of a function that has been shifted vertically you add or subtract the vertical shift 2 from the altered range based on the amplitude. Sine and cosine transformations the coefficients a and b in y asin bx or y acos bx each have a different effect on the graph. The graph of a sinusoidal function has the same general shape as a sine or cosine function.

Sine and cosine transformations.