Trigonometry and Unit Circle Review

4.6 Day 2, 4.7 and Unit Circle Review

-Graphing Tangent and Cotangent

-Inverse Trig Functions

-Unit Circle

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

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 $$\degree$$ - 90 $$\degree$$  

radians: 0 - $$\pi$$ / 2  

Review of Inverse Trig Functions 

y = arcsin (x)
D: [-1, 1]
R: [- $\pi$ / 2 , $\pi$ / 2]
y = arccos (x)
D: [-1, 1]

R: [0 , $\pi$ ]

y = arctan (x)

D: (- $\infty$  , $\infty$ )

R: [- $\pi$ / 2, $\pi$ / 2]   

Inverse Trig Functions

What questions do you have about the 4.7 notes video?

Let's discuss and make some more connections.

Multiple Choice

sin ( $$\pi$$ / 6 ) = 

• $$\sqrt{ }$$ 3 / 2
  

• 1/2

•  $\sqrt{ }$ 3 / 2

•  $\sqrt{ }$ 2 / 2

Multiple Choice

arcsin(1/2)

• $$\pi$$ / 3

• - $\pi$ / 3

• $\pi$ / 6

• - $\pi$ / 6

Multiple Choice

arctan (- $$\sqrt{ }$$ 3) =

• $$\sqrt{ }$$ / 3

• - $\pi$ / 3

•  $\pi$ / 6

• - $\pi$ / 6

Multiple Choice

tan ( $$\pi$$ / 6 ) = 

• $$\sqrt{ }$$ 3 

•  $\sqrt{ }$ 3 / 3

• 1

Multiple Choice

arcsin (5 $$\pi$$ / 2) 

•  $\pi$ / 2 

• 0

• 1

• No Solution / Undefined

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

Review of Tangent and Cotangent

- Cotangent is the reciprocal of Tangent

cot $\theta$ = 1 / tan $\theta$  

                = cos $\theta$ / sin $\theta$  

 
 tan $\theta$ = sin $\theta$ / cos $\theta$  

Tangent and Cotangent Graphing on Desmos link

https://www.desmos.com/calculator/cxffgjxejh

Multiple Choice

Is this a tangent or cotangent graph?

• tangent

• cotangent

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 $$\pi$$

• 1/2 $\pi$

• $\pi$

• 1/4 $\pi$

Multiple Choice

What is equation for the vertical asymptotes of y = cot (3x)? (Graph corresponds to y = cot (3x) equation)

• x = 1/3 $$\pi$$ n

• x = 3 $\pi$ n

• x = 1/3 $\pi$ + $\pi$ n

• x = 3 $\pi$ + $\pi$ n

Open Ended

Find arcsin(-1/2) =