Graphing Cosine and Sine FunctionsObj: graph sine and cosine on graph paper and

notebook paper

Without any notes, give the following ratios.

sin 135⁰ cos 180⁰ cos 300⁰ sin 150⁰ cos 225⁰ sin 60⁰

QUIZ SOON!! Get out your unit circle from your notes.

We can take the circular graph and “unroll” it to graph sin x and cos x on a linear graph.

Check out the x-axis on your graph paper.

Notice how the x-axis has radian measures from -2π to 2π. You cannot see the increment of π/6, but there is a tick mark for it. Make sure you can locate it on the graph.

The y values are not marked yet. The dotted line above the x-axis is 1 and below the x-axis is -1.

Now using your circle graph, we are going to take the sine values from the circle and put them on the linear graph.

So start at 0 radians. At 0, the sine value is 0, so put a point at (0, 0) on the linear graph.

Moving around the circle, at π/6, the sine value is ½, so put a point at (π/6, ½).

At π/4, sine is 1/√2. Using your calculator, find an approximation for 1/√2. Plot the point.

Continue around the circle until you have plotted all of the points. Connect the dots.

The graph has NO sharp points!

The graph has NO straight edges!

This will always be a nice smooth curve.

The max value is 1, the min value is -1. Every value between is on the graph.

When graphing trig functions without graph paper, ALWAYS label four tick marks on the x-axis and 2 on the y-axis.

Label the x-axis from 0 to 2π and the y-axis from -1 to 1.

Then put points on the curve at the quadrantal angles. Connect the points with a smooth curve. Remember no sharp points and no straight edges.

It should look like this…

Find all values of x such that 0 < x < 2π and sin x = 1.

X = π/2

Extend your graph on the interval to -2π.

Find 4 values of x such that sin x = 1.x = π/2, 5π/2, -3π/2, -7π/2

Find all values of x such that sin x = 1.x = π/2 + 2πk

Now graph the cosine values on the graph paper.

Do the same on your notebook paper.

Consider the graph y = sin(x + π/2)

Sine and cosine are both periodic functions because they conclude one full cycle within a specific period.

What is the period of y = sin x?2π

What is the period of y = cos x?2π

What is the period of your intellectual cycle?emotional?physical?

In groups of 2 on one sheet of paper, do problems 1 – 4 on page 16. When finished, compare with other 2 in your group.Turn in.

On your own, do problems 7 – 16. These are due next class period.