Math 2412 – Precalculus
Section 5.1 The Unit Circle
Please review Section 5.1. Work all examples in the text.
The unit circle is a circle centered at (0, 0) with radius 1 unit. x2 + y2 = 1
Every point on the unit circle is called a
point (1, 0). Move counterclockwise if t > 0 and clockwise if t < 0.
The circumference of the unit circle is C =
π
What is the terminal point for t = ?
4
Can use similar methods to find terminal points for other t values.
. Let t be any real number. Start at
Math 2412
Ex: Suppose the point P
Section 5.1 Continued
√ !
3
, y is on the unit circle, in Quadrant I. Find y.
2
We can fill in the entire unit circle using quadrant I.
2
Math 2412
Section 5.1 Continued
Ex: Find the terminal point determined by t.
π
(a) t = −
4
(b) t =
5π
6
Definition: Let t be a real number. The reference number associated with t is the shortest distance along the
unit circle between the terminal point and the x−axis.
4 cases:
Using reference numbers to find terminal points:
1. Find the reference number
2. Find the terminal point determined by the reference number
3. Determine the signs for the x and y coordinates based upon the quadrant where the point lies.
Ex: Find the reference number and terminal point.
5π
(a) t =
2
(c) t =
(b) t = −
4π
3
(d) t =
3
13π
4
31π
6