Transcript Document
TRIGONOMETRIC RATIOS AND THE UNIT CIRCLE
Mrs. White Precalculus 5.2/5.4
Schedule
Class/Week
Mon 2/3 Tues 2/4 Wed 2/5 Thurs 2/6 Fri 2/7
Topic
The Unit Circle 5.2
Exact Values of the Trig Ratios Exact Values of the Trig Ratios Exact Values of the Trig Ratios
Class Work
Complete the Unit Circle Template Examples/Notes
Homework
Pg 361 # 3 -30 Multiples of 3 Pg. 383 # 3, 14, 18, 22, 34, 39, 43, 54 Study for Quiz 5.2
Review and Practice Worksheet 5.2
(No calculator) Quiz (No Calculator) Watch Video on Graphs of Sine/Cosine
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) Θ (radians)
sin
Θ
cos
Θ
tan
Θ
csc
Θ
sec
Θ
cot
Θ 0 0 o
0 1 0 Undefined 1 Undefined
30 o π /6 45 o π /4
1
60 o π /3 90 o π /2
1 0 Undefined 1 Undefined 0
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
cos
5 13 12 13
tan
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
cos
tan
5 29 29 2 5
Example 3
Given the following, find the 6 trigonometric ratios: sec Θ = -2 sin Θ > 0
sin cos
tan
3 2 2 1 3
Example 4
Find the reference angle,
α
.
Given: Θ = 309 o
α
= 360 o - 309 o
α
= 51 o Find the reference angle,
α
.
Given: Θ = 11 3 Θ
α
= = 11 3 2 1 2 5 1 3 5 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 510
o
1 2 cos 510
o
2 3 tan 510
o
3 3 csc 510
o
2 sec 510
o
cot 510
o
2 3 3 3
Example 6
Evaluate the 6 trig functions of the following angles. No Calculator.
11 Θ = This is coterminal with: Reference angle:
,
Quadrant 3 sin 4 11 2 4 3 4 csc 11 2 cos 4 11 4 11 2 2 2 sec 4 11 2 tan 1 cot 4 11 1 4 4
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 2 3 Θ