EOC review Unit 7 and 8

EOC review Unit 7 and 8

Unit 7 Circles

• Equations of Circles - complete the square

• Angles and Arcs in circles

• Segments and lines in circle

• Arc Length and Area Sector

Circle Equations

(x-h)² + (y-k)² = r²

Center - (h, k) *remember insiders lie

radius is r *take the square root of the number on the end

Completing the Square:

Organize the equation to have x's together and y's together and constants on the other side of the equal sign

*divide the middle term by 2 and square it

*Add that number to both sides of the equation

*factor the trinomials by dividing the middle term by 2

Multiple Choice

A circle has the equation  
x² + y² - 12x + 8y + 3 = 0.  Write the equation in standard form.

• (x - 6)² + (y + 4)² = 49
• (x + 4)² + (y - 6)² = 49
• (x - 6)² + (y + 4)² = 55
• x² + y² = 55

Multiple Choice

Calculate the value of x.

• 13
• 14
• 15
• 16

Multiple Choice

What is the value of y? Round to the nearest whole number.

• 16
• 17
• 18
• 19

Multiple Choice

What is the value of c? Round to the nearest whole number.

• 2
• 3
• 4
• 5

Multiple Choice

What is the measure of angle HKI?

• 72
• 73
• 74
• 75

Multiple Choice

What is the measure of angle QRP?

• 23
• 24
• 22
• 21

Multiple Choice

What is the measure of arc NM?

• 116
• 117
• 118
• 119

Arc Length and Sector Area

Arc Length =  $\frac{\theta}{360}2\pi r$   

Area of Sector =  $\frac{\theta}{360}\pi r^2$  

Multiple Choice

What is the measure of arc KL?

• 108

• 106

• 110

• 112

Unit 8 Trig

• Converting radians and degrees

• Unit Circle

• Quadrants

• Graphing trig functions

Conversions

• 180 degrees = $\pi$   radians

• To convert from degree to radians - multiply by  $\frac{\pi}{180\degree}$  

• To convert from radian to degree- multiply by  $\frac{180\degree}{\pi}$  

• 
  

Multiple Choice

What is  $270\degree$  in radians?

• $\frac{\pi}{4}$

• $\frac{3\pi}{2}$

• $\frac{3\pi}{4}$

• $\frac{\pi}{2}$

Multiple Choice

What is $\frac{2\pi}{3}$   radians in degrees? 

•  $150\degree$  

•  $120\degree$  

•  $180\degree$  

•  $30\degree$  

Multiple Choice

What is  $\frac{11\pi}{6}$   radians in degrees? 

• 30

• 330

• 360

•  300

Multiple Choice

What is  $225\degree$   in radians? 

•  $\frac{7\pi}{4}$  

•  $\frac{5\pi}{4}$  

•  $\frac{3\pi}{4}$  

•  $\frac{5\pi}{3}$  

Multiple Choice

What is the radius of the unit circle?

• 0
• 1
• 1/2
• √2/2

Multiple Choice

Based on the unit circle, what is the value of tan?

• y/r
• x/r
• r/y
• y/x

Multiple Choice

Based on the unit circle, what is the value of cos?

• y

• x

• x/y

• y/x

Multiple Choice

Based on the unit circle, what is the value of sin?

• y

• x

• x/y

• y/x

Multiple Choice

What is the best estimated of the red angle?

• 90

• 45

• 135

Multiple Choice

sinθ is positive in

• the 1st and 2nd quadrants
• the 1st and 3rd quadrants
• the 1st and 4th quadrants
• the 2nd and 3rd quadrants

Multiple Choice

cosθ is positive in

• the 1st and 2nd quadrants
• the 1st and 3rd quadrants
• the 1st and 4th quadrants
• the 2nd and 3rd quadrants

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 Choice

• -1
• 0
• undefined
• √3

Multiple Choice

• √3/3
• √3
• 1
• undefined

Multiple Choice

cos 4π/3

• -√3/2
• √3/2
• 1/2
• -1/2

Multiple Choice

What is the value of cosine at 270

• 0
• 1
• -1

Multiple Choice

What is the value of sine at 210?

• 1/2
• -1/2
• √3 / 2
• -√3 / 2

Multiple Choice

What is the value of cosine at 135

• 0
• 1/2
• √2 /2
• -√2 /2

Graphing Sine and Cosine

• y=asin(bx)+d

• a = amplitude (radius of the circle)

• b = frequency (how many times a cycle repeats between 0 and 2 $\pi$ )

• d = midline (how high the center of the circle is from the ground) - constant

• Period =  $\frac{2\pi}{b}\ or\ \frac{2\pi}{freq}$  (time it takes to travel around a circle)

Multiple Choice

Who are these ladies?

• The Golden Girls
• The Old Timers
• Betty White and Sisters
• Facts of Life Girls

Multiple Choice

State the midline of the function.
 $f\left(x\right)=\frac{1}{2}\cos\ x-5$  

•  $y=5$  

•  $y=-\frac{1}{2}$  

•  $y=\frac{1}{2}$  

•  $y=-5$  

Multiple Choice

State the midline of the function.
 $f\left(x\right)=2\sin\ x+3$  

•  $y=2$  

•  $y=-3$  

•  $y=3$  

•  $y=-2$  

Multiple Choice

What is the equation of the graph?

• y = - 6 cos x - 1
• y = 3 cos x - 4
• y = -7 cos x 
• y = -3 cos x - 4 

Multiple Choice

What is the amplitude of this function?

• 2
• 2π
• -2
• 1

Multiple Choice

What is the equation of graph? 

• y = sin 5x
• y =  cos 5x
• y = 5 sin x
• y = 5 cos x 

Multiple Choice

What is the period of the graph? 

• 2Pi
• Pi
• Pi/2
• Pi/4 

Multiple Choice

What is the amplitude of the graph?

• -2

• 2

• 4

• 1

Multiple Choice

What is the period of
y= 4 cos (5x)

• 2π/5
• π
• 5
• 5π

Multiple Choice

what is the amplitude of
y = 3sin (7x) -2

• 7
• -2
• 3
• 6

Multiple Choice

What is the period of either graph? 
y = sin(x)      &   y = cos (x)

• Pi
• 2Pi
• Pi/2
• Pi/4 

Multiple Choice

Where does the graph of cosine begin?

• (0,0)
• (0,1)
• (0, Pi)
• (1, Pi)

Multiple Choice

Where does the graph of y=sin(x) begin its first cycle?

• (0,0)
• (1,0)
• (0,Pi)
• (1, Pi)

Multiple Choice

What is the measure of arc AB?

• 140
• 142
• 180
• 153

Multiple Choice

Alison is jogging on a circular track that has a radius of 140 feet.  She runs along the track from point R to point N, a distance of 230 feet. Find to the nearest degree, the measure of minor arc RN.

• 47
• 74
• 94
• 123

Multiple Choice

When she is outdoors, Tasha, the dog, is tied to a stake in the center of a circular area of radius 24 feet. The angle between her dog house and her favorite hydrant is 165 degrees.  What is the length of the arc from her dog house to the hydrant, following minor arc DG, to the nearest foot.

• 40
• 35
• 55
• 69

Multiple Choice

What is the area of the shaded sector?

• 439.12 in²

• 113.04 in²

• 339.29 in²

• None of the above

Multiple Choice

Find the area of each sector.

• 52.4 in²
• 18,864 in²
• 60 in2
• 10.47 in

Multiple Choice

What is the radius of the given circle:
 x²+y²-10x+8y-23=0?

• 4
• 2
• 8

Multiple Choice

Write the standard equation of the circle with the given center and radius; center (0,0) and radius: 3

• x²+y²=3
• x²+y²=6
• x²+y²=9

Multiple Choice

In the equation (x-4)²+(x-3)²=25, the center of the circle is at...

• (-3, -4)
• (4, 3)
• (-4, -3)
• (3, 4)

Multiple Choice

According to a proverb about hope, "There's always light at the end of..." what?

• The journey
• The day
• The tunnel
• E.T.'s finger