Download 30-1 Unit Circle

Math 30-1
Trigonometric Functions
Radians in Standard Position
(The Unit Circle)
Part 1: Radian Measure of the Special Angles
The diagram below shows all the multiples of 30° (solid lines) and 45° (dashed lines) in standard
position. Label each angle in degrees. Then convert every degree measure to radians and write
the radian measure beside the degree measure.
Math 30-1
Trigonometric Functions

What do you notice about the radian measure of all the angles with a 30° reference angle?
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What do you notice about the radian measure of all the angles with a 45° reference angle?
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What do you notice about the radian measure of all the angles with a 60° reference angle?
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What do you notice about the radian measure of all the angles with a 0° reference angle?
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What do you notice about the radian measure of all the angles with a 90° reference angle?
Part 2: Coordinates of the Unit Circle
The circle on the front of this page is a unit circle with the equation x 2  y 2  1 . (Remember:
this means that the radius is 1.) Write the coordinates of the point on the terminal arm of each
angle in standard position.

How do the coordinates of each point relate to the sine and cosine ratio of each angle?
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How can you find the tangent ratio of the central angle if you know the coordinates of a point
of the unit circle?

Describe any patterns you see in the coordinates of the points on the unit circle.