trigonometric ratios and the unit circle mrs. white precalculus 5.2/5.4
TRANSCRIPT
TRIGONOMETRIC RATIOS AND THE UNIT CIRCLEMrs. WhitePrecalculus 5.2/5.4
Schedule
Class/Week Topic Class Work Homework
Mon 2/3 The Unit Circle5.2
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 PracticeWorksheet 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 1 Undefined
csc Θ Undefined 1
sec Θ 1 Undefined
cot Θ 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.
5
1312
135
12
sin
cos
tan
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.
2 29
29
5 29
292
5
sin
cos
tan
Example 3
Given the following, find the 6 trigonometric ratios: sec Θ = -2 sin Θ > 0
3
21
2
3
sin
cos
tan
Example 4
Find the reference angle, α.
Given: Θ = 309o
α = 360o - 309o
α = 51o
Find the reference angle, α.
Given: Θ =
Θ =
α =
11
3
11 2 5
3 1 3
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
1sin 510
2
3cos 510
2
3tan 510
3
o
o
o
csc 510 2
2 3sec 510
3
cot 510 3
o
o
o
Example 6
Evaluate the 6 trig functions of the following angles. No Calculator.
Θ = This is coterminal with: Reference angle: , Quadrant 3
11
4
3
4
4
11csc 2
411
sec 24
11cot 1
4
11 2sin
4 2
11 2cos
4 211
tan 14
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: Θ
3sin
2