The Unit Circle Worksheet With Answers By Ana Zuniga (Page 10 of 12) in pdf

The Unit Circle Worksheet With Answers By Ana Zuniga Page 10

Unit Circle Project Directions

On a poster board, draw the unit circle. It must include the angle measures in both degrees and radians.

You must also include the coordinates at each point. It must cover most of the poster. Then choose five

points (none that are on the axes, so not 90, 180, or 270 degrees) and draw five separate circles. For

each circle show ALL work for deriving the coordinates of that angle measure, including any rationalizing

that you do. See the example below.

Your project must be neat. Your angle measurements should be precise and use your creativity in

presenting your project (bright colors, etc.). Attach the grading rubric to the back of your project.

Example: Let’s say I’m going to show the derivation for 135 degrees (3π/4), then I would go to that

point, drop a perpendicular towards the x-axis thus forming a right triangle. The hypotenuse measures 1

(because it’s the unit circle and the radius is one). The central angle at this point (the reference angle)

measures 45 degrees (180 – 135 = 45 degrees). Therefore, this is a 45-45-90 special right triangle. Then

use the rules of the 45-45-90 to explain why the coordinates at this point are (-

This is a 45-45-90 triangle.

Both legs measure the same

since it’s an isosceles right

triangle. Because the

hypotenuse is 1, then to go

from the hypotenuse to the

leg I have to divide by

Because you can’t be left

with radicals in the

denominator, I must then

rationalize by multiplying

both numerator and

denominator by

Each

side therefore measures

Since 135 degrees is located in

the second quadrant, the x-

coordinate must be negative.

Hence, that’s why the

coordinates at this point are

The Unit Circle Worksheet With Answers By Ana Zuniga Page 10