Questions asked by Jennifer

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• What is the angular velocity of the second hand of a clock, in radians per second?
  
• A car is travelling 44 feet per second (30 miles/hour). What is the angular velocity of its 22 inch diameter wheels, in revolutions per minute?
  
• Two countries are halfway around the world from each other (by E to W) and lie on the 17 degree north latitude. Earth's radius is 3790 miles at that latitude. Would flying west to the other country be shorter, or would flying directly north be shorter?
  
• Ferris wheel=123ft tall; 1rev./2min. Central angle theta form arc PA. What is the height of P as a function of time? Assume position A corresponds to t = 0.
  
• A water pipe bends in a circular arc changing direction by 23.7 degrees. The curved portion is 47.2 ft long. What is the radius of the circle?
  
• What is (1-cotx)(1+cotx)-csc^2x?
  
• Verify these identities? sin^2x-tan^2x = -sin^2xtan^2x 1/(secx-tanx) = tanx+secx
  
• What are all the values for A between 0 to 360 degrees? sinA+1=tanA+cosA
  
• What are all values for A between 0-360 degrees? sin^2(A/2)=cos^2A
  
• A tunnels arch is parabola shaped. It spans 8 meters wide, and is 5 meters high at a distance of 1 meter from the tunnel's edge. What is the maximum height of the tunnel?
  
• What is the equation of this curve with P given? The difference of the distance between P(x,y) and the points (-2,1) and (8,1) is 6.
  
• A hyperbola's center is at (1,-3). a^2 is 4 and b^2 is 16. How would I know if the hyperbola is horizontal or vertical? Can't it be both?
  
• What is the polar equation with the same graph as (x+2)^2 + (y-1)^2 = 5?
  
• Can someone verify this? (cotx-1)/(cotx+1) = (1-sin2x)/(cos2x)