Question

Jack is on a carousel at the rodeo. The diameter of the carousel is 80 feet. Find the position of Jack's seat in point form from the center of the carousel after a rotation of 210 degrees. Explain why the angle you use in the equation is not 2100. Write the two equations you used to set up the problem. the position of Jack's seat is: _______________________Give the exact answer (no rounding).

Answer 1

Answer:

1) The reason, the 210° angle is not used is because, the values of the trigonometric ratios for 210° is the same as the values of the trigonometric ratios for 30°

2) The two equations used to set up the problem are;

The y-coordinate value, y₁ = -40×sin(30°) = -20 feet

The x-coordinate value, x₁ = 40×cos(30°) = 34.64 feet

3) The coordinates of the point location of Jack's seat = (20×√3, -20)

Step-by-step explanation:

The given information are;

The diameter of the carousel = 80 feet

The rotation of the carousel = 210°

Assuming Jack seat was initially on the left side of the center of the carousel and the carousel rotates clockwise, we have;

Final position of the carousel = 210 - 180 = 30° South of East

The radius of the carousel = (80 feet)/2 = 40 feet

The slope of the location of Jack seat = -tan(30°)

The y-intercept = The center = 0

y - y₁ = m·(x - x₁)

The y-coordinate value, y₁ = -40×sin(30°) = -20 feet

The x-coordinate value, x₁ = 40×cos(30°) = 20×√3 = 34.64 feet

The equation in point and slope form is therefore;

y - (-20) = -√3/3×(x -  34.64)

y + 20 = -x·√3/3 + 20

y = -x·√3/3

The reason, the 210° angle is not used is because, the values of the trigonometric ratios for 210° is the same as the values of the trigonometric ratios for 30°

The two equations used to set up the problem are;

The y-coordinate value, y₁ = -40×sin(30°) = -20 feet

The x-coordinate value, x₁ = 40×cos(30°) = 34.64 feet

The coordinates of the point location of Jack's seat = (20×√3, -20)