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 =  $\frac{2\pi}{period}$  

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

 $\tan\left(t\right)$  

•  $\sqrt{3}$  

•  $\frac{\sqrt{3}}{3}$  

•  $\frac{1}{2}$  

•  $\frac{\sqrt{3}}{2}$