#4 All Trignometric Graphs

The __________ represents half the distance between the max and min of a sine or cosine graph.

• Period

• Frequency

• Asymptotes

• Amplitude

What is the period of this equation?
 $y=-5\sin\left(3x\right)$  

• -5

•  $\frac{2\pi}{3}$  

•  $\frac{2\pi}{5}$  

• 3

Tags

CCSS.HSF-IF.C.7E

What is the amplitude of the graph? 

• 1
• 3
• 6
• 9

• $f\left(x\right)=3\sin x$

• $f\left(x\right)=3\cos x$

• $f\left(x\right)=\ \sin\left(\frac{1}{3}x\right)$

• $f\left(x\right)=\ \cos\left(\frac{1}{3}x\right)$

Which value helps identify a vertical shift in the following function  $y=\pm a\sin\left(\omega\left(x-h\right)\right)+k$  

• a

•  $\omega$  

• h

• k

Which function below matches this graph?

• $\frac{1}{2}\tan x$

• $\tan\left(\frac{1}{2}x\right)$

• $-\frac{1}{2}\tan\ x$

• $-\frac{1}{2}\tan\left(\frac{1}{2}x\right)$

What is the domain and range of y=sinx?

• D: (-∞, ∞)
  R: [-1, 1]
  
• D: (-∞, ∞)
  R: [-π, π]
• D: (∞, -∞)
  R: [1, -1]
  
• D: (-∞, ∞)
  R: [-∞, ∞]
  

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.B.5

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.4

Which function below describes only the following transformations?

Reflection over x-axis
Horizontal stretch by 2

• 
  

   $y=\sin(-2x)$  

•  $y=-\sin(\frac{1}{2}x)$  
  

•  $y=-\tan\left(2x\right)$ 

•  $y=\frac{-1}{2}\tan\left(x\right)$  
  

What is the equation of the graph?

• $y=2\cos x$

• $y=\sin x$

• $y=2\sin x$

• $y=\sin2x$

The period of a sine graph in the form  $y=\pm a\sin\left(\omega\left(x-h\right)\right)+k$  

• is always  $2\pi$  

•  $\frac{2\pi}{\omega}$  

•  $\omega$  

•  $\frac{h}{\omega}$