The Figure Below Illust X G An arctic valage maint x XC Chegg study I Guided x L

Question

The Figure Below Illust X G An arctic valage maint x XC Chegg study I Guided x L x D Pathways iMathAS Ass x tps/Vimathas rational reasoning-net, ies nt/showtest.php? action-skip&to; 7&reattempt; 7 toys cecar travels along a circular path with center (0.0. The racecar begins at 9.0) and travels 31 meters ter-clockwise on a circular path with an 9 meter radius. Line racecar stops at the point (z, y). 31 meters a Determine the measure of the angle (in radians) that is formed by the ray connecting (0,0 to (9.0) and the ray connecting (0.0) and (r, y) radians Preview b. Determine the values of r and y measused in meters un temas ofthe sine and or cosine functions tabu doc dreamworks co jpg SONY

Explanation / Answer

a. Arc defined by the angle = 31 m

Radius of the circle = [(9-0)2+(0-0)2] = 9m

1 radian is the angle subtended by an arc of length 9m.

Thus the angle subtended by arc of length 31m

= 31*1/9 = 31/9 radians.

b. If we draw a line from (x,y) paralell to x axis, it will meet the y axis at (0,y)

Let us observe the triangle formed by (x,y), (0,0) and (0,y).

The triangle has sides equal to x, y and (x2+y2).

The angle made by the line connecting (x,y) and (0,0) with the line connecting (0,0) and (0,y) is

2 - 31/9 - /2 = 3/2 -31/9 radians

Thus x = 9 sin(3/2 -31/9) radians .

y = 9 cos(3/2 -31/9) radians.

c. x = 9 sin(3/2 -31/9) = 8.6

However, since x lies in the third quadrant, x = -8.6

y = 9 cos(3/2 -31/9) = 2.684

However, since y lies in the third quadrant, y = -2.7

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