Question 1087512: I NEED HELP ASAP WITH TRIGONOMETRIC FUNCTIONS AND INVERSES
A communication satellite is orbiting the Earth at a height of h miles above the planet's surface. The satellite can transmit data to any point along an arch length s miles on the Earth based on the "line of sight" from the satellite to the point on the arc. At the endpoints of the arc, the line of sight from the Earth, (assume the Earth is a sphere of radius 3960 mi). Let theta represent one-half of the central angle subtended by the arc as shown in the diagram at right.
a)express the angle theta as a function of h
b)express the length of the arc, s, as a function of theta. (don't forget about radian measure)
c)use composition of functions to find the length of the arc, s, as a function of h.
d)since the angle and the arc length are both functions of the height of the satellite, it is this height that determines their values. Build a table for both functions showing their values for heights ranging from 0 to 1000 miles in increments of 100 miles.
e)try using some values of h greater than 1000 to see what happens to theta and s, then discuss, intuitively, (using common sense), what the angle, theta, and the arc length, s, approach as h increases to infinity. Now, relate these ideas to the terms "domain" and "range".
I DON'T KNOW HOW TO ADD THE IMAGE...
I did try to do these on my own however, I think I may have misunderstood the original question so my other answers are incorrect.
a) cos(theta)= r/r+h --> cos^-1(cos theta)= cos^-1(r/r+h) -->
theta=cos^-1(r/r+h) --> substitute the radius in--> theta=cos^-1(3960/3960+h)
b) s=r(theta) --> plug in radius --> s=3960(theta)
c) s=3960(theta) -->substitute--> s=3960*cos^-1(3960/3960+h)
Answer by Fombitz(32388)   (Show Source):
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