EOC Review of 7 & 8

EOC Review of 7 & 8

EYNTK Review

- "Everything You Need To Know"

Unit 7: EYNTK

• Equation of a circle:

   $\left(x-h\right)^2+\left(y-k\right)^2=r^2$  where (h, k): center & r: radius

• How To Find: use completing the square!

Angles of Circles

• Central Angle: measure of CA = measure of Arc

• Inscribed Angle: measure of IA = ½ of the measure of arc

• Exterior Angle: (Big Arc-Little Arc)/2

• Interior Angle: ½(measure of arc CD + measure of arc AB)

Segments in Circles

Arc Length & Area of a Sector

• Arc Length: portion of circumference

• Arc Length: $2\pi r\left(\frac{n}{360}\right)$  

• Area of a sector: portion of the area of a circle

• Area of Sector:  $\left(\frac{n}{360}\right)\pi r^2$  

Unit 8: EYNTK

• Degrees $\rightarrow$ Radians:  $n\degree\ \times\frac{\pi}{180}$  

• Radians $\rightarrow$ Degrees:  $n\pi\times\frac{180}{\pi}$  

• where  $n\degree\ \&\ n\pi$  are any angles

Unit Circle

•  $\left(x,\ y\right)=\left(\cos\theta,\ \sin\theta\right)$ A

•  $\tan\theta=\frac{\sin\theta}{\cos\theta}=\frac{y}{x}$  

• All functions are positive in 2 quadrants &  negative in 2 quadrants

• Positive Angles: counterclockwise

• Negative Angles: clockwise

Sine & Cosine Graphs

•  $y=amp\cdot\sin\left(freq\cdot x\right)+midline$  

• Amplitude: height of the wave from the midline

• Frequency: how many times a wave occurs in $2\pi$  

• Period: length of one wave,  $\frac{2\pi}{frequency}$  

• Midline: the average line of the wave

Sine & Cosine Applications

• Amplitude = $\frac{\max-\min}{2}$  

  
  

• Midline = $\frac{\max+\min}{2}$  

• Frequency =  $\frac{2\pi}{period}$  

Fill in the Blank

Solve for x. Round to the nearest whole number.

Fill in the Blank

What is the measure of angle BAC

Fill in the Blank

What is the arc length?

Fill in the Blank

What is the value of x?

Fill in the Blank

What is the measure of arc AC?

Multiple Choice

What is the period of this sine graph?

• $2\pi$

• $\pi$

• $\frac{\pi}{2}$

• $\frac{3\pi}{2}$

Multiple Choice

A ferris wheel's diameter is 40 ft and makes 1 revolution in 30 seconds. The center of the wheel is 30 feet above the ground. If a person taking a ride starts at the lowest point, which trigonometric function can be used to model the rider’s height h(t) above the ground after t seconds?

• $h\left(t\right)=-20\cos\left(\frac{\pi}{15}t\right)+30$

• $h\left(t\right)=-40\cos\left(\frac{\pi}{15}t\right)+10$

Multiple Choice

What is the frequency of

 $y=-2\cos\left(x\right)+4$  

• 4

• 2

• 1

•  $\pi$  

Multiple Select

If

 $\sin\left(x\right)=\cos\left(x\right)$  , what quadrants could the angle terminate in?

• I

• II

• III

• IV

Multiple Choice

What is the

 $\tan\left(t\right)$  

•  $\sqrt{3}$  

•  $\frac{\sqrt{3}}{3}$  

•  $\frac{1}{2}$  

•  $\frac{\sqrt{3}}{2}$