ne X dsLearning20sine20and20cosinepdf 2 Sheldon is playing w

ne X ds/Learning%20sine%20and%20cosine.pdf 2. Sheldon is playing with his toy train set. The train begins at (3.5,0) and travels 25 meters counter-clockwise on a circular path with an 3.5-meter radius. The racecar stops at the point (x,y). a. Determine the measure of the angle (in radians) that is formed by the ray Explain in words how you got the answer. b. Determine the values of x y in terms of the sine and cosine function, and then and determine their decimal approximations in meters using your calculator. Explain in words how you got the answer. your variables. c. 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 25 meters. Define your variables. d. 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.

Solution

2) train starts at (3.5,0) and goes till (x,y)

radius = 3.5

arc length = 25 metres

therefore applying the formula of arc length

arc length = RC

C = 25/3.5 = 7.1428

angle = 7.1428 radians

it stops at (x,y)

so formula to find x component is

x = r cos theta

y component is

y = r sin theta

the value can be calculated by plugging the values

x = r cos theta = 3.5 cos 7.1428 = 2.2844

y = r sin theta = 2.6515