#### Transcript of 4.05b Analyzing the Sine and Cosine Functions

Domain

The domain is the allowed values that theta can take. There is no restriction on theta and therefore it can be any real number: (-infinity, infinity)

X-intercepts

The x-intercepts are where the graph of the cosine function will cross or touch the x-axis. Since cosine is a periodic function it will cut the x axis infinite number of times. On the positive side it will cut the x axis at: pi/2, 3pi/2, 5pi/2, ....

And on the negative side it will cut the x axis at: -pi/2, -3pi/2, -5pi/2, ....

We can combine them and say the x-intercepts are:

π2±kπ

where k = 0, 1, 2, 3, .... (k is any integer)

Period

Amplitude

The cosine function is a periodic function meaning the function repeats itself after every period. The period of cosine function is: 2(pi). So after every + or - 2(pi) the curve would repeat itself and will look exactly alike.

Range

As mentioned earlier, the cosine function oscillates between -1 and +1. Therefore, the range of the cosine function is: [-1, 1]

(Notice we use brackets [ ] in specifying range and not parenthesis ( ). Brackets because the end values -1 and +1 are both INCLUDED in the range.

The amplitude of this cosine function is 1. It means the function has a maximum value of 1 and a minimum value of -1 and when plotted the curve will look like a wave oscillating between those two values.

f(theta) = cos(theta)

Citations :)

**4.05b Analyzing the Sine and Cosine Functions**

-The book provided.

-Pre-calculus book Custom edition for university of North Florida.

And these 2 videos. It would just let me put the links.

Describe each of the following properties of the graph of the Cosine Function, f(theta) = cos(theta) and relate the property to the unit circle definition of cosine.

Choice #1

**Made by: Kayla Larson :) hope you enjoy!! **

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