Graph Tangent and Cotangent

4.6 Day 2 - Graphing Tangent and Cotangent

-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.

Multiple Choice

ACT Practice Problem:

Ms. Baker began her math class by saying:

I’m thinking of 5 numbers such that their mean is equal to their median. If 4 of the numbers are 14, 8, 16, and 14, what is the 5th number?

What is the 5th number Ms. Hernandez is thinking of?

• 13

• 14

• 15

• 16

• 18

Review of Tangent and Cotangent

- Cotangent is the reciprocal of Tangent
ie. cot $\theta$  = 1 / tan $\theta$ 
 

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

Tangent and Cotangent Graphing on Desmos link

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

Open Ended

What is the equation for the vertical asymptote of y = cot (1/2x)?

Open Ended

What are the vertical asymptote equations for Tangent and Cotangent (from video and important ideas section on the notes)

Multiple Choice

What is the period of y = tan (2x) ?

•  $\pi$ / 2

•  $\pi$ 

• 3 $\pi$ / 2

• 2 $\pi$ 

Open Ended

What is the period of y = cot (1/4x) ?

Multiple Choice

What is the equation for the vertical asymptote of y = tan (1/2x)?

• x = $$\pi$$ + 2 $$\pi$$ n

• x = $\pi$ /2 + $\pi$ n

• x = $\pi$ +2 $\pi$ n

• x = 2 $\pi$ + $\pi$ n

Open Ended

Is this a tangent or cotangent graph?

Open Ended

What is the period of this graph?

Open Ended

Write out 3 vertical asymptotes you see on this graph

Open Ended

What is the equation of this graph

Multiple Choice

What is the equation of the graph?

• y = tan (2x) + 5

• y = tan (x) - 5

• y = tan (1/2x) - 5

• y = tan (1/2x) + 5

Multiple Choice

What is the correct equation of a tangent function with a period of $$\pi$$ / 2 that is shifted up 2 and shifted to the left  $$\pi$$ / 3.

• y = tan (2x + $\pi$ / 3) + 2

• y = 2 tan (x + $\pi$ / 3) - 2

• y = tan (2x - $\pi$ / 3) - 2

• y = 2 tan (2x - $\pi$ / 3) + 2