Graphs of Circular Functions Help (page 3)

By — McGraw-Hill Professional
Updated on Oct 3, 2011

Practice 2

What is the range of the function described above?

Solution 2

Look at the drawing you made, showing the graph of the function. The range of this function is represented by the portion of the y axis for which the function is defined: all the values y such that y is between 0 and 1, inclusive. Formally, if we call B* the range of this function, we can write

B * = { y : 0 ≤ y ≤ 1}

Practice 3

The domain of the sine function is the same as the domain of the cosine function. In addition, the ranges of the two functions are the same. How can this be true, and yet the two functions are not identical?

Solution 3

The difference, as you can see by comparing the graphs of the two functions, is that the curves are displaced along the x axis by 90° (π/2 rad). In general, the cosine of a number is not the same as the sine of that number, although there are certain specific instances in which the two functions have the same value.

Practice 4

Draw a graph that shows the specific points where sin x = cos x.

Solution 4

This can be done by superimposing the sine wave and the cosine wave on the same set of coordinates, as shown in Fig. 3-7. The functions attain the same value where the curves intersect.

Graphs and Inverses Inverses of Circular Functions

Fig. 3-7 . Illustration for Solution 4, showing points where the sine and cosine functions attain the same y value.

Practice Problems for these concepts can be found at:  Graphs and Inverse Practice Test

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