Radians and Degrees
Areas and Sectors
Gears and Latitudes
Linear and Angular Speed
Random
100

what is  (9pi)/10 in degrees?

162 degrees

100

What are the equations to find the area of a sector of a circle and length of an arc? (in radians)

Arc =(s)=rtheta

Area=1/2pir^2

100

What do all connected gears have in common? What is the relationships between 2 gears and their central angles and radii given they aren't the same size?

The arc length is equal no matter what the angle of rotation is. The gear with the larger radius should always the smaller angle of rotation.

100

Write all the forms of linear and angular equations relating to speed (should be 3 for velocity)

V=S/T=(rtheta)/T=rw

w=theta/T

100

What part of a butterfly 'tastes'?

Its feet.

200

if the minute hand of a clock has rotated 40 minutes, what is that in radians?

(4pi)/3rad

200

if a circle has an arc length of  15pi and a central angle of  (5pi)/6 , what is the radius?

15pi=r*(5pi)/6=>18

200

If  city_1 is  (3pi)/8 rad above the equator, and  city_2 is  (3pi)/8 rad below the equator:

How far apart are they if the earth has a radius of 6400 km?

(3pi)/8 rad+(3pi)/8 rad=(6pi)/8 rad

(6pi)/8 rad * 6400 km = 4800pi km

200

What are the units of Linear and Angular speed?

Linear speed is distance/time and angular speed is radians/time.

200

How many teeth does the average human have?

32

300

What are sin, cos and tan of  (7pi)/4 ?

Sin((7pi)/4)=-sqrt2/2; Cos((7pi)/4)=sqrt2/2; tan((7pi)/4)=-1

300

If a circle has a diameter of 12 ft and a central angle of  (5pi)/4 rad , what is the area of the sector?

Area=(5pi)/4*6ft=(45pi)/2 ft

300

Gear1 has a radius of 4 cm and rotates  (5pi)/4 rad . If gear2 rotates  (5pi)/3 rad , what is its radius? Explain how you know your answer makes sense.

(5pi)/4 rad* 4cm=5picm

5picm=(5pi)/3*r=>r=3cm

Because it has a larger degree of rotation, the radius should be smaller than 4.

300

Turn  (4ft)/(1sec) into  (mi)/(hr) . Write as a decimal with units.

(4ft)/(1sec)*(60sec)/(1min)*(60min)/(1hr)*(1mi)/(5280ft)=(2.73mi)/(1hr)

300

Name the last 3 Super Bowl winners.

Kansas City, Kansas City, Los angeles

400

Using pizza slices, explain how slices there are and find the equivalent angles in each quadrant to  pi/7 .

There should be 14 slices since we cut each half into 7.

Q_1=pi/7; Q_2=(6pi)/7;Q_3=(8pi)/7;Q_4=(13pi)/7

400

A circle has an area of  33pi cm^2 and a central angle of  (11pi)/6 rad . Find its radius.

33picm^2=(1/2)(11pi)/6r^2=>r=6cm

400

Gear1  has a radius of 8 cm and rotates  (2pi)/3  and Gear2 has a radius of 6. How much does gear 2 rotate?

Gear1: 

8cm*(2pi)/3=(16picm)/3

Gear2: 

(16picm)/3=(6cm)/(1rad)theta=>theta=(8pi)/9 rad

Smaller radius for gear 2, therefore it must have a larger central angle.

400

The distance from the sun to the earth is around 93,000,000 km.

1. What is earth's angular speed around the sun?

2. What is earth's linear speed relative to the sun?

1. 

w=(2pirad)/(365days)

2. 

V=rw=(93,000,000)/(1rad)*(2pi rad)/(365days)*(day)/(24hr)=67,000(mi)/(hr)


400

Draw your groupmates when they were babies.

Goo goo.

500

How many radians does the hour hand of a clock turn in 4 days? 10 days? half a day?

The hour hand rotates around the clock 2 times per day. So, 1 day is

(4pi rad)/(1 day)

Therefore: 4 days is 16pi rad, 10 days is 40pi rad and half a day is 2 pi rad.

500

Given the arc of a circle is  16pi and has a central angle of  (4pi)/3 , find the area of the sector of the circle formed by the same arc.

Arc: 16pi=r*(4pi)/3=>r=12

Area=(1/2)(4pi)/3(12)^2=96pi

500

If  city_1 is  (pi)/3 rad above the equator, and  city_2 is  (pi)/6 rad above the equator:

How far apart are they if the earth has a radius of 6400 km?

(pi)/3 rad-(pi)/6 rad=(pi)/6 rad

(pi)/6 rad * 6400 km = (3200pi)/3 km

500

What is an asymptote?

A horizontal of vertical line that a function doesn't cross.