The path of a toy racecar that begins at (6, 0) and travels 30 meters counter-cl

Question

The path of a toy racecar that begins at (6, 0) and travels 30 meters counter-clockwise on a circular path with an 6-meter radius. The racecar stops at the point (xy). Determine the measure of the angle (in radians) that is formed by the ray connecting (0.0) to (6.0) and the ray connecting (0.0) to (xy). Explain in words how you got the answer. Determine the values of x and y in terms of the sine and cosine function, and then determine their decimal approximations in meters using your calculator. Explain in words how you got the answer. Define your variables. Define a formula that relates the horizontal component x (in radii) in terms of the number of meters d the racecar has traveled along the track. After you are done. evaluate your function for a value of 30 meters. Define your variables Define a formula that relates the vertical component y (in meters) in terms of the number of meters d the racecar has traveled along the track. Define your variables.

Explanation / Answer

Point(6,0) to ( x, y) ; Arc length = 30 mt

radius = 6 mt

i)Angle = arc length/radius = 30/6 = 5 radians

ii) Apply trigonometric ratio :

sin(theta) = y/r = sin(5)

y = r*sin(5) = 6sin(5) = -5.75

costheta = x/r

x = rcostheta = 6cos(5) = 1.70

c) y = rsintheta = r*sin(d/r)

= 6sin(30/6)

d) x = rcostheta = r*cos(d/r)

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