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TRIGONOMETRIC RATIOS
AND THE UNIT CIRCLE
Mrs. White
Precalculus 5.2/5.4
Schedule
Class/Week
Topic
Class Work
Homework
Mon 2/3
The Unit Circle
5.2
Complete the Unit Circle
Template
Pg 361 # 3 -30
Multiples of 3
Tues 2/4
Exact Values of the Trig
Ratios
Examples/Notes
Pg. 383 # 3, 14, 18, 22,
34, 39, 43, 54
Wed 2/5
Exact Values of the Trig
Ratios
Review and Practice
Worksheet 5.2
(No calculator)
Study for Quiz 5.2
Thurs 2/6
Exact Values of the Trig
Ratios
Quiz
(No Calculator)
Watch Video on Graphs
of Sine/Cosine
Fri 2/7
Trig Ratios and the Unit Circle

Goals

Students should be able to calculate the
exact value of the 6 trigonometric ratios.
Review – Complete the Table
Θ (degrees)
0o
30o
45o
60o
90o
Θ (radians)
0
π/6
π/4
π/3
π/2
sin Θ
0
1
cos Θ
1
0
tan Θ
0
csc Θ
Undefined
1
sec Θ
1
Undefined
cot Θ
Undefined
0
1
Undefined
Example 1

Plot P (-12, -5) in the
coordinate plane. If
the terminal side of an
angle in standard
position passes through
P, find the 6 trig.
Ratios.
sin  
5
13
co s  
12
13
ta n  
5
12
Example 2

Plot P (5, -2) in the
coordinate plane. If
the terminal side of an
angle in standard
position passes through
P, find the 6 trig.
Ratios.
sin  
2 29
29
co s  
5 29
29
ta n  
2
5
Example 3

Given the following,
find the 6
trigonometric ratios:
 sec
Θ = -2
 sin Θ > 0
sin  
co s  
3
2
1
2
ta n    3
Example 4



Find the reference
angle, α.
Given:
Θ = 309o



Find the reference
angle, α.
Given:
Θ = 11
3

α = 360o - 309o

Θ = 11
3

α = 51o


2
1

5
3
α = 2   5  
1
3
3
Example 5




Evaluate the 6 trig functions of the following angles.
No Calculator.
Θ = 510°
This is coterminal with: 150°
Reference angle: 30°, Quadrant 2
sin 5 1 0 
o
1
csc 510  2
o
2
co s 5 1 0  
o
3
2
tan 5 1 0  
o
3
3
sec 510  
o
2 3
3
cot 510   3
o
Example 6




Evaluate the 6 trig functions of the following angles.
No Calculator.
11

Θ= 4
3

This is coterminal with:
4
Reference angle:  , Quadrant 3
sin
 1 1
4

4
co s
tan
 1 1
4
 1 1
4
2
csc
2

2
sec
2
1
cot
 11
4
 11
4
 11
4
 2
 2
1
Example 7


Sketch a right triangle corresponding to the trig
function of the acute angle, Θ. Find the length of
the missing side (using Pythagorean Th). Evaluate
the remaining 5 trig. functions at Θ.
Given: sin  
3
2
Θ

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