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)
