<< Chapter < Page Chapter >> Page >

A satellite is rotating around Earth at 0.25 radian per hour at an altitude of 242 km above Earth. If the radius of Earth is 6378 kilometers, find the linear speed of the satellite in kilometers per hour.

1655 kilometers per hour

Got questions? Get instant answers now!

Key equations

arc length s = r θ
area of a sector A = 1 2 θ r 2
angular speed ω = θ t
linear speed v = s t
linear speed related to angular speed v = r ω

Key concepts

  • An angle is formed from the union of two rays, by keeping the initial side fixed and rotating the terminal side. The amount of rotation determines the measure of the angle.
  • An angle is in standard position if its vertex is at the origin and its initial side lies along the positive x -axis. A positive angle is measured counterclockwise from the initial side and a negative angle is measured clockwise.
  • To draw an angle in standard position, draw the initial side along the positive x -axis and then place the terminal side according to the fraction of a full rotation the angle represents. See [link] .
  • In addition to degrees, the measure of an angle can be described in radians. See [link] .
  • To convert between degrees and radians, use the proportion θ 180 = θ R π . See [link] and [link] .
  • Two angles that have the same terminal side are called coterminal angles.
  • We can find coterminal angles by adding or subtracting 360° or 2 π . See [link] and [link] .
  • Coterminal angles can be found using radians just as they are for degrees. See [link] .
  • The length of a circular arc is a fraction of the circumference of the entire circle. See [link] .
  • The area of sector is a fraction of the area of the entire circle. See [link] .
  • An object moving in a circular path has both linear and angular speed.
  • The angular speed of an object traveling in a circular path is the measure of the angle through which it turns in a unit of time. See [link] .
  • The linear speed of an object traveling along a circular path is the distance it travels in a unit of time. See [link] .

Section exercises

Verbal

Draw an angle in standard position. Label the vertex, initial side, and terminal side.


Graph of a circle with an angle inscribed, showing the initial side, terminal side, and vertex.

Got questions? Get instant answers now!

Explain why there are an infinite number of angles that are coterminal to a certain angle.

Got questions? Get instant answers now!

State what a positive or negative angle signifies, and explain how to draw each.

Whether the angle is positive or negative determines the direction. A positive angle is drawn in the counterclockwise direction, and a negative angle is drawn in the clockwise direction.

Got questions? Get instant answers now!

How does radian measure of an angle compare to the degree measure? Include an explanation of 1 radian in your paragraph.

Got questions? Get instant answers now!

Explain the differences between linear speed and angular speed when describing motion along a circular path.

Linear speed is a measurement found by calculating distance of an arc compared to time. Angular speed is a measurement found by calculating the angle of an arc compared to time.

Got questions? Get instant answers now!

Questions & Answers

A laser rangefinder is locked on a comet approaching Earth. The distance g(x), in kilometers, of the comet after x days, for x in the interval 0 to 30 days, is given by g(x)=250,000csc(π30x). Graph g(x) on the interval [0, 35]. Evaluate g(5)  and interpret the information. What is the minimum distance between the comet and Earth? When does this occur? To which constant in the equation does this correspond? Find and discuss the meaning of any vertical asymptotes.
Kaitlyn Reply
The sequence is {1,-1,1-1.....} has
amit Reply
circular region of radious
Kainat Reply
how can we solve this problem
Joel Reply
Sin(A+B) = sinBcosA+cosBsinA
Eseka Reply
Prove it
Eseka
Please prove it
Eseka
hi
Joel
June needs 45 gallons of punch. 2 different coolers. Bigger cooler is 5 times as large as smaller cooler. How many gallons in each cooler?
Arleathia Reply
7.5 and 37.5
Nando
find the sum of 28th term of the AP 3+10+17+---------
Prince Reply
I think you should say "28 terms" instead of "28th term"
Vedant
the 28th term is 175
Nando
192
Kenneth
if sequence sn is a such that sn>0 for all n and lim sn=0than prove that lim (s1 s2............ sn) ke hole power n =n
SANDESH Reply
write down the polynomial function with root 1/3,2,-3 with solution
Gift Reply
if A and B are subspaces of V prove that (A+B)/B=A/(A-B)
Pream Reply
write down the value of each of the following in surd form a)cos(-65°) b)sin(-180°)c)tan(225°)d)tan(135°)
Oroke Reply
Prove that (sinA/1-cosA - 1-cosA/sinA) (cosA/1-sinA - 1-sinA/cosA) = 4
kiruba Reply
what is the answer to dividing negative index
Morosi Reply
In a triangle ABC prove that. (b+c)cosA+(c+a)cosB+(a+b)cisC=a+b+c.
Shivam Reply
give me the waec 2019 questions
Aaron Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

Ask