Download Name:___________________________________ Date:________Period:_______ _______________________

Name:___________________________________
Date:________Period:_______
Chapter 8: Basic Trigonometry
Topic 4: Unit Circle Introduction
The _______________________ is a circle with a radius of 1 and a center (0,0)
For a point (x,y) in Quadrant I, the lengths x and y become the legs of a right triangle whose
hypotenuse is 1. By the Pythagorean Theorem, we have x2 + y2 = 1
(the equation of the unit circle).
If we examine angle θ (in standard position) in this unit
circle, we can see that ..........
cosθ = ______
sinθ = ______
On the unit circle (x, y) = (
,
)
Think: In terms of sinθ and cosθ, what do you think
tanθ will be equal to?
tanθ = _______
Unit circle with radius of length___.
Label the quadrantal angles and the coordinates of each.
0⁰
sinθ
cosθ
tanθ
90⁰
180⁰
270⁰
360⁰
Examining the Unit Circle
All Students Take Calculus
As point (x, y) moves around the unit circle, and θ increases from 0° to 360°, x and y change
signs and thus the signs of sinθ and cosθ also change.
In the first quadrant, since x and y are both positive numbers, sinθ is positive and cosθ is
positive.
In the second quadrant, since x is a negative number and y is a positive number, sinθ is
positive and cosθ is negative.
In the third quadrant, since x and y are both negative numbers, sinθ is negative and cosθ is
negative.
In the fourth quadrant, since x is a positive number and y is a negative number, sinθ is
negative and cosθ is positive.
Identify the quadrant that each angle θ could lie in.
1)
2)
3)
4)
Draw a picture
Label ASTC
Put a check in the quadrants that satisfy the conditions
Choose the correct quadrant
1. sin θ > 0 and cosθ > 0
2. sin θ < 0 and cos θ > 0
3. sin θ < 0 and tanθ > 0
4. sin θ > 0 and cos θ < 0
5. tan θ > 0 and sin θ > 0
7. cos θ > 0 & tan θ < 0
6. sin θ < 0 and c os θ > 0
The terminal side of <ROP is in standard position and intersects the unit circle at point P. If
<ROP is θ, find:
a) sinθ
b) cosθ
c) Quadrant of <ROP
if...
1)
2)
a) sinθ
a) sinθ
b) cosθ
b) cosθ
c) Quadrant of <ROP
c) Quadrant of <ROP
1) P(-0.25,-0.23)
2) P(0.6,-0.8)
3)
a) sinθ
a) sinθ
a) sinθ
b) cosθ
b) cosθ
b) cosθ
c) Quadrant of <ROP
c) Quadrant of <ROP
c) Quad of <ROP