7.4 Graphs of Trigonometric Functions

In the graph of y = sinx, we are examining the relationship between an angle in standard position, x, versus the sine of that angle, y. These two pieces of information are considered together in the form (x, y)

We use the unit circle to examine this relationship. As x increases from 0 to π/2, the value of y increases from 0 to 1. We continue examining this trend for any value of x we want.

Some notes about y = sinx:

• The domain is any real number

• The range is -1 to 1
• The function is periodic

A periodic function is a function that repeats itself on a set interval.

What is the period for y = sinx? (ie what is the length, in x, before the function repeats itself)

We can also use the unit circle to examine the relationship of y = cosx. As x increases from 0 to π/2, the value of y decreases from 1 to 0.

Some notes about y = cosx:

• The domain is any real number

• the range is -1 to 1
• the function is periodic, with a period of

In order to examine y = tanx, we first need to learn a trig identity. An identity is an equation that is true for all values.

Use the values of x, y, and r to prove that tanx = sinx / cosx

Now that we know that this is true, we can use the unit circle to discuss the relationship y = tanx

Some notes about y = tanx

• The domain is any real number except kπ/2, where k is an odd number.

• the range is any real number
• the function is periodic, with a period of