Prepared: Thu May 6 18:11:18 CDT 1999

QUIZ V

1) Given that and , determine the other five trigonometric functions.

First observe that means that lies in the fourth quadrant. Since , there is a point whose y-coordinate is -12 and distance from origin is 13.

However, we still need the x-coordinate of the point to write down all the trigonometric functions. Now, recall that

In our case then

So we have

Since the angle is in the fourth quadrant, its x-coordinate should be positive, i.e x=5.

Now recall the definitions of the trigonometric functions of an angle in terms of x, y and r.

2) Sketch the graph of for .

Observe that the graph of y is the graph of sin(t) shifted units right and 4 units up. (Important: 4 is NOT the amplitude!)

3) Sketch the graph of for .

First find the amplitude and period.

Before we try to find the (h,k), the shift parameters, we need to do a little change in the style that y is written. Rewrite y in a better style:

Now we can safely say that
"The graph of y is merely the graph of shifted units right.",
in other words .

We choose the second method to graph y. We first move the origin units right and then plot the graph in the main region with t ranging from to , and y ranging from -2 to 2.

Now we repeat that picture for the rest.

4) The terminal side of the angle passes through (-12, 8). Determine the values of the , and .

Given information tells us that x=-12 and y=8. So we need only the distance from the origin to find the expected values. But recall that

So we have

Using the definition of sin, cos tan in terms of coordinates and distance from the origin of the point gives