MATH 140-Pre Caleulus One-a-Day 15 Amgle Measure I. You have walked far enough a
ID: 3018563 • Letter: M
Question
MATH 140-Pre Caleulus One-a-Day 15 Amgle Measure I. You have walked far enough along a unit circle to have walked 0.1745 units. What angle have subtended? you 2. Find an angle between 0° and 360° coterminal with 10000 3. Find the length of an arc that subtends a central angle of 38" in a circle of radius 15 fed 4. An arc of length 100m subtends a central angle n a circle of radius 1 10m. Find the measure of@in degrees. S. Memphis, Tennessee, and New Orleans, Louisiana, lie approximately on the same meridian. Memphis has latitude 3S "N and New Orleans, 30°N. Find the distance between these two cities. (The radius of the earth is 3960 miles)Explanation / Answer
1)
Arc length = 0.1745 units
Radius, r = 1 unit
And using s = r * theta, we have
0.1745 = 1 * theta
theta = 0.1745 radians or 9.9981 degrees
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2)
Coterminal with 10000
We keep subtracting 360, or any multiple of it
10000 - 360x say
0 < 10000 - 360x < 360
0 > 360x - 10000 > 360
10000 > 360x > 10360
27.7777777777777778 > x > 28.7777777777777778
So, consider 27
9720
Now, subtract
10000 - 9720
280 degrees ---> ANS
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3)
Theta = 38 deg or 38*pi/180 radians
Radius, r = 15 ft
s = r * theta
s = 15 * 38pi/180
s = 9.9483767363676786 ft
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4)
s = r * theta where theta is in radians...
100 = theta * 110
theta = 100/110 radians
theta =10/11 * 180/pi degrees
= 52.087 degrees
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