If θ measures 0 radians, what is the measure of the angle with an initial ray in the 3 o'clock position and a terminal ray passing through the car? radians   If θ measures 1 radians, what is the measure of the angle with an initial ray in the 3 o'clock position and a terminal ray passing through the car? radians   cos(1)= 0.5403023058681398. For any value θ, what is the measure of the angle with an initial ray in the 3 o'clock position and a terminal ray passing through the car? radians

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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  1. If θ measures 0 radians, what is the measure of the angle with an initial ray in the 3 o'clock position and a terminal ray passing through the car?

    radians  

  2. If θ measures 1 radians, what is the measure of the angle with an initial ray in the 3 o'clock position and a terminal ray passing through the car?

    radians   cos(1)= 0.5403023058681398.

  3. For any value θ, what is the measure of the angle with an initial ray in the 3 o'clock position and a terminal ray passing through the car?

    radians  

 

 

Answer the following questions.
a. If 0 measures 0 radians, what is the measure of the angle with an initial ray in the 3 o'clock position and a terminal ray passing through the
car?
cos(0)
* radians
Preview
b. If 0 measures 1 radians, what is the measure of the angle with an initial ray in the 3 o'clock position and a terminal ray passing through the
car?
cos(1)
radians
Preview
cos(1) = 0.5403023058681398.
c. For any value 0, what is the measure of the angle with an initial ray in the 3 o'clock position and a terminal ray passing through the car?
theta
* radians
Preview
Transcribed Image Text:Answer the following questions. a. If 0 measures 0 radians, what is the measure of the angle with an initial ray in the 3 o'clock position and a terminal ray passing through the car? cos(0) * radians Preview b. If 0 measures 1 radians, what is the measure of the angle with an initial ray in the 3 o'clock position and a terminal ray passing through the car? cos(1) radians Preview cos(1) = 0.5403023058681398. c. For any value 0, what is the measure of the angle with an initial ray in the 3 o'clock position and a terminal ray passing through the car? theta * radians Preview
Example 1: Toy Cars (Different Starting Positions)
A toy racecar is racing on a circular race track. The car is 2.5 feet from the center of the race track and travels in the CCW direction. However,
this racecar starts at the 12-0’clock position. 0 is the measure of the angle shown (in radians).
We need to be a little cautious in this scenario, because now 0 doesn't represent a number of radians swept out from the 3-o'clock position.
Instead, 0 represents a number of radians swept out from the 12-o'clock position.
0 = 6.28
You might feel tempted to write the expressions 2.5 cos(0) and 2.5 sin(0) to model the car's position relative to the center of the race track. Let's
check and see if these expressions work.
a. Compute 2.5 cos(0) and 2.5 sin(0) for 0
0.
о 2.5 сos(0) -
= 2.5cos(0)
Preview
o 2.5 sin(0)
2.5sin(0)
Preview
Transcribed Image Text:Example 1: Toy Cars (Different Starting Positions) A toy racecar is racing on a circular race track. The car is 2.5 feet from the center of the race track and travels in the CCW direction. However, this racecar starts at the 12-0’clock position. 0 is the measure of the angle shown (in radians). We need to be a little cautious in this scenario, because now 0 doesn't represent a number of radians swept out from the 3-o'clock position. Instead, 0 represents a number of radians swept out from the 12-o'clock position. 0 = 6.28 You might feel tempted to write the expressions 2.5 cos(0) and 2.5 sin(0) to model the car's position relative to the center of the race track. Let's check and see if these expressions work. a. Compute 2.5 cos(0) and 2.5 sin(0) for 0 0. о 2.5 сos(0) - = 2.5cos(0) Preview o 2.5 sin(0) 2.5sin(0) Preview
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