Tangent function CVU2024

Tangent Function
(Turn to notes page 34)

recall what we discussed about tangent last term.. goodluck ! :)

Multiple Choice

Tangent is the ratio of the...

• ...the opposite side to the adjacent side for a given angle measurement.

• ...the adjacent side to the opposite side for a given angle measurement.

• ...the adjacent side to the hypotenuse for a given angle measurement.

• ...the opposite side to the hypotenuse for a given angle measurement.

Multiple Choice

Which of the following best describes Tangent?

• Tangent is the distance for a given angle measurement.

• Tangent is the rise and run for a given angle measurement.

• Tangent is the midpoint for a given angle measurement.

• Tangent is the size of a given angle measurement.

Multiple Choice

tanθ is positive in

• the 1st and 2nd quadrants

• the 1st and 3rd quadrants

• the 1st and 4th quadrants

• the 2nd and 3rd quadrants

Multiple Select

$$\tan\left(\theta\right)$$  of an angle,  $$\theta$$ can be expressed as which of the following?

• $$\frac{opposite}{hypotenuse}$$  

• $$\frac{opposite}{adjacent}$$  

• $$\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$$  

• $$\frac{hypotenuse}{adjacent}$$  

Multiple Choice

tan (-π)

• undefined
• 0
• 1
• -1

Multiple Choice

tan(45^o)

• √2/2
• 1/2
• √3/2
• 1

Multiple Choice

tan(270^o)

• 1
• -1
• 0
• undefined

Multiple Choice

Name two angles with tangent 0.

• 45^o and 225^o
• 135^o and 315^o
• 0^o and 180^o
• 90^o and 270^o

Multiple Choice

What is the tangent of 7π/4?

• -√2/2

• 1

• √2/2

• -1

Multiple Choice

Use the calculator to find tan 60

• .87

• 1.7

• .5

• .11

Multiple Choice

Which value is NOT defined?

• $$\tan0$$

• $$\tan\left(\frac{\pi}{2}\right)$$

• $$\tan\left(\frac{2\pi}{3}\right)$$

• $$\tan\left(2\pi\right)$$

Multiple Choice

What's the vertical translation of this graph?

• down 2

• up 2

• up 5

• no vertical translation

Multiple Choice

What is the range of the graph of a tangent function?

• (-∞, ∞)

• [-1, 1]

• (0, ∞)

• (-∞, 0)

Multiple Choice

What are the vertical assymptotes of $$y=\tan x$$ over its first cycle?

• $$x=0\ and\ x=2\pi$$  

• $$\ x=\frac{\pi}{2}\ and\ x=\frac{3\pi}{2}$$  

• $$x=\sqrt{3}\ and\ x=-3$$  

• $$\ x=\frac{\pi}{2}\ and\ x=2\pi$$  

Multiple Choice

What is the exact value of $$\tan\left(\frac{2\pi}{3}\right)$$  

• $$\frac{2}{\sqrt{3}}$$  

• $$\frac{\sqrt{2}}{2}$$  

• $$-\sqrt{3}$$  

• $$-\frac{\sqrt{3}}{3}$$  

Multiple Choice

Write the equation for a tangent function with a = 6 and a period of π/4.

• y=6tan(8x)

• y=6tan(4x)

• y=6tan1/4x

• y=6tanx

Multiple Choice

What is the equation of the graph shown?

• $$y=\tan\left(\frac{1}{2}x\right)$$

• $$y=\tan\left(2x\right)$$

• $$y=\tan\left(\frac{1}{4}x\right)$$

• $$y=\tan\left(4x\right)$$

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 amplitude of tangent?

• Tangent has no amplitude

• always 1

• always $$\pi$$

• It varies with each graph

Multiple Choice

What is the period of y=4tan5x

• π/5

• π

• 5

• 5π

• 2π/5

All done! do the exercises and..

see you soon!