Quiz Review Basics of SIne and Cosine

Quiz Review Basics of SIne and Cosine

Sine Curve Questions

Multiple Select

What color points have the coordinates

 $\left(x,\frac{\sqrt{3}}{2}\right)\ or\ \left(x,\frac{-\sqrt{3}}{2}\right)\$  

• black

• blue

• green

• red

• none of these

Answer

These are the RED Points

Multiple Select

What color points have the coordinates

 $\left(x,\frac{\sqrt{2}}{2}\right)\ or\ \left(x,\frac{-\sqrt{2}}{2}\right)\$  

• black

• blue

• green

• red

• none of these

Answer

These are the GREEN Points

Multiple Select

What color points have the coordinates

 $\left(x,\frac{\sqrt{3}}{2}\right)\ or\ \left(x,\frac{-\sqrt{3}}{2}\right)\$  

• black

• blue

• green

• red

• none of these

Answer

These are the BLUE Points

Multiple Select

What color points have the coordinates

 $\left(x,1\right)\ or\ \left(x,-1\right)\$  

• black

• blue

• green

• red

• none of these

Answer

These are the WHITE Points

(None of these)

Multiple Select

What color points have the coordinates

 $\left(x,0\right)$  

• black

• blue

• green

• red

• none of these

Answer

These are the BLACK Points

Fill in the Blanks

What letter represents the following point?

 $\left(30\degree,\frac{1}{2}\right)$  

Answer

Point I is

 $\left(30\degree,\frac{1}{2}\right)$  

Multiple Select

Which statement is false about the sine function?

• midline is the x axis

• the origin lies on this graph

• range = 2

• domain is

  $360\degree$

• none of these statements are false

Answer

Domain is 360 degrees is a FALSE Statement

None of these are False is a FALSE Statement

Period = 360 degrees

Domain = all real numbers

Multiple Select

Which statement is false about the sine function?

• One period  $\left[0\degree,360\degree\right)$  

• The range is  $\left(-1,1\right)$  

• The range is  $\left[-1,1\right]$  

• Sine Function increases over  $\left[0\degree,90\degree\right)\ \ OR\ \ \left(270\degree,360\degree\right]$  

Answer

range is (-1.1) is a FALSE statement because the range can reach -1 and 1 so correct range is [-1, 1]

Multiple Select

Which is the amplitude of sine function?

• 180

• 1

• -1

• 1 or -1 

• 360

Answer

Amplitude measures the distance from the midline (in this case the x axis) to the extreme values on the graph of sine at W and E

Amplitude is 1

Cosine Curve Questions

Multiple Select

What color points have the coordinates

 $\left(x,\frac{\sqrt{2}}{2}\right)\ or\ \left(x,\frac{-\sqrt{2}}{2}\right)\$  

• black

• blue

• green

• red

• none of these

Answer

The green points represent

 $\left(x,\frac{\sqrt{2}}{2}\right)\ or\ \left(x,\frac{-\sqrt{2}}{2}\right)\$  

Multiple Select

What color points have the coordinates

 $\left(x,1\right)\ or\ \left(x,-1\right)\$  

• black

• blue

• green

• red

• none of these

Answer

The black points represent

 $\left(x,1\right)\ or\ \left(x,-1\right)\$  

Multiple Select

What color points have the coordinates

 $\left(x,\frac{\sqrt{3}}{2}\right)\ or\ \left(x,\frac{-\sqrt{3}}{2}\right)\$  

• black

• blue

• green

• red

• none of these

Answer

The blue points represent

 $\left(x,\frac{\sqrt{3}}{2}\right)\ or\ \left(x,-\frac{\sqrt{3}}{2}\right)\$  

Multiple Select

What color points have the coordinates

 $\left(x,\ 0\right)\$  

• black

• blue

• green

• red

• none of these

Answer

None of these

The white points represent

 $\left(x,0\right)$  

Fill in the Blanks

What letter represents the coordinate

 $\left(300,\ \frac{1}{2}\right)\$  

Answer

The point P represents (300, 0.5)

Multiple Select

Which of the following statements is false?

• all x intercepts of cosine take the form

  $\left(90+90n,0\right)$ provided that n is an integer

• all x intercepts of cosine take the form $\left(90n,0\right)$ provided that n is an integer

• all x intercepts of cosine take the form $\left(90+180n,0\right)$ provided that n is an integer

Answer

all x intercepts of cosine take the form

(90+180n,0)

 provided that n is an integer

90-180(-2) = 90-360= -270

90-180(-1) = 90-180= -90

90-180(0) = 90+0= 90

90-180(1) = 90+180= 270

90-180(2) = 90+360= 450

Multiple Select

What has changed in the red graph compared to the normal cosine graph on the left?

• the domain

• the period

• the amplitude

• the midline

• nothing has changed

Answer

the period of cosine is normally [0,360)

the red graph has a period of [0,120)

Multiple Select

What has changed in the red graph compared to the normal cosine graph on the left?

• the domain

• the period

• the amplitude

• the midline

• nothing has changed

Answer

the period of cosine is normally [0,360)

the red graph has a period of [0,240)

the midline is normally y = 0, in this case it is y = 1