

Trigonometry and Unit Circle Review
Presentation
•
Mathematics
•
11th - 12th Grade
•
Hard
Joseph Anderson
FREE Resource
8 Slides • 10 Questions
1
4.6 Day 2, 4.7 and Unit Circle Review
-Graphing Tangent and Cotangent
-Inverse Trig Functions
-Unit Circle

2
Lesson Goals
Understand how asymptote equations are found for tangent, and cotangent by finding when the function in the denominator is equal to 0
Graph and write tangent and cotangent equations and identify the period and asymptote equations
Explain why and how the domains of sine, cosine, and tangent must be restricted to create an inverse function
Evaluate inverse trig expressions and equations
Fill in blank unit circle
3
Open Ended
WARMUP!
The unit circle is divided into four quadrants. What are the angle and radian values for each quadrant.
write out answers like this:
ex. Q1:
degrees: 0 ° - 90 °
4
Review of Inverse Trig Functions
y = arcsin (x)
D: [-1, 1]
R: [- π / 2 , π / 2]
y = arccos (x)
D: [-1, 1]
R: [0 , π ]
y = arctan (x)
D: (- ∞ , ∞ )
R: [- π / 2, π / 2]
5
Inverse Trig Functions
What questions do you have about the 4.7 notes video?
Let's discuss and make some more connections.
6
7
Multiple Choice
sin ( π / 6 ) =
3 / 2
1/2
3 / 2
2 / 2
8
Multiple Choice
arcsin(1/2)
π / 3
- π / 3
π / 6
- π / 6
9
Multiple Choice
arctan (- 3) =
/ 3
- π / 3
π / 6
- π / 6
10
Multiple Choice
tan ( π / 6 ) =
3
3 / 3
1
11
Multiple Choice
arcsin (5 π / 2)
π / 2
0
1
No Solution / Undefined
12
Unit Circle
Let's practice filling in the unit circle by memory.
Lets do 10 minutes of practice by using this online activity:
https://www.mathwarehouse.com/unit-circle/unit-circle-game.php
13
Review of Tangent and Cotangent
- Cotangent is the reciprocal of Tangent
cot θ = 1 / tan θ
= cos θ / sin θ
tan θ = sin θ / cos θ
14
Tangent and Cotangent Graphing on Desmos link
https://www.desmos.com/calculator/cxffgjxejh
15
Multiple Choice
Is this a tangent or cotangent graph?
tangent
cotangent
16
Multiple Choice
What is the period of y = tan (1/2x)?
(Hint: use "B = horizontal stretch / shrink" from the 4.5 day 2 notes, don't need to look at the graph to find the period. You can calculate it with the period formula)
Period = Period of Parent Function / B
2 π
1/2 π
π
1/4 π
17
Multiple Choice
What is equation for the vertical asymptotes of y = cot (3x)? (Graph corresponds to y = cot (3x) equation)
x = 1/3 π n
x = 3 π n
x = 1/3 π + π n
x = 3 π + π n
18
Open Ended
Find arcsin(-1/2) =
4.6 Day 2, 4.7 and Unit Circle Review
-Graphing Tangent and Cotangent
-Inverse Trig Functions
-Unit Circle

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