A race car is driven around a circular track at a constant speed of 180mph. If the diameter is 1/2 mile, what is the angular speed of the car? Express your answer in revolutions per hour.
The formula for angular speed is w=theta (in radians)/time
Find the value of each of the remaining trig functions.
Cscθ=-4, π< θ<3π/2
To find the angular speed of the car, we first need to convert the constant speed of the car from miles per hour to radians per hour.
1. We know that 1 revolution is equal to 2π radians (a full circle is 2π radians).
2. The circumference of the circular track can be found using the formula C = πd, where d is the diameter. In this case, the diameter is 1/2 mile, so the circumference is C = π * (1/2) = π/2 miles.
3. Since the car is driving at a constant speed of 180 mph, it covers a distance of 180 miles per hour.
4. We can divide this distance by the circumference of the track to find the number of revolutions per hour: 180 miles / (π/2 miles) = (360/π) revolutions per hour.
Therefore, the angular speed of the car is (360/π) revolutions per hour.