The Unit Circle

To use the unit circle, first identify the trig function. Each one has a different formula.
Sin: y/r Csc: r/y
Cos: x/r Sec: r/x

Tan: y/x Cot: x/y

The unit circle is a circle with the center (0,0) and a radius of 1.

For instance, if you were to find sine of 90 degrees, you would look at your unit circle and find 90 degrees at (0,1). Then you would use the formula for sine (y/r) and plug in your y(1) and your radius(1). This gives you 1/1, or 1. This tells you that the answer is positive. If your answer has a 0 as denominator, it is undefined. You might also be given radians instead of degrees, in which case you convert to degrees and plot the point the same way. If your degree is greater than 360, use a reference angle. When plotting the point, if the degree value given is negative, rotate the same amount of degrees clockwise instead of counterclockwise to find your point.

____________________________________________________________

Examples:

1. Find whether the following are positive or negative.

a.) sin 165 degrees (y/r) = positive number/1 = Positive.

We know it the y is positive because when you graph

165 degrees, it is in the second quadrant.

b.) cos 210 degrees (x/r) = negative number/1 = Negative.

This answer is negative because the angle is in the third quadrant.

2. Find sine, cosine, and tangent.

a.) sin 90 degrees (y/r) = 1/1 = 1

b.) cos 270 degrees (x/r) = 0/1 = 0

c.) tan -90 degrees (y/x) = -1/0 = undefined