1. The height the end of the pump arm is above the ground is given by the equation H = 6 + 4Sin(πt) Oil Pump Problem where t = time in minutes And H is the vertical height in metres When is the height first 2.8 metres above the ground? Method A Method B Method C Height ‘H’ Method D

2. Oil Pump method A Solve 2.8 = 6 + 4Sin(πt) -0.8 = Sin(πt) = 0.927 πt = π + 0.927 Calculate Sin -1 0.8 The height the end of the pump arm is above the ground is given by the equation H = 6 + 4Sin(πt) where t = time in minutes And H is the vertical height in metres When is the height first 2.8 metres above the ground? Height ‘H’ -3.2 = 4Sin(πt) π 0, 2π A TC S Ignore negative Negative Sin so Quadrant 3 & 4 t = 1.295 min Quadrant 3 πt = 4.0689 RADIANS! Home

3. Oil Pump method B Solve 2.8 = 6 + 4Sin(A) -0.8 = Sin(A) = 0.927 A = π + 0.927 Calculate Sin -1 0.8 The height the end of the pump arm is above the ground is given by the equation H = 6 + 4Sin(πt) where t = time in minutes And H is the vertical height in metres When is the height first 2.8 metres above the ground? Height ‘H’ -3.2 = 4Sin(A) π 0, 2π A TC S Ignore negative Negative Sin so Quadrant 3 & 4 = 1.295 min Quadrant 3 A = 4.0689 Let A = πt And t = A ÷ π t = 4.0689 ÷ π Solve 2.8 = 6 + 4Sin(πt) RADIANS! Home

4. Oil Pump method C Solve 2.8 = 6 + 4Sin(πt) -0.8 = Sin(A) A = π + 0.927 t = 4.0689 ÷ π (A) = Sin -1 -0.8 The height the end of the pump arm is above the ground is given by the equation H = 6 + 4Sin(πt) where t = time in minutes And H is the vertical height in metres When is the height first 2.8 metres above the ground? Height ‘H’ -3.2 = 4Sin(A) Sketch the graph t = 1.295 min A = -0.927 Below 0 so next highest solution? Let A = πt Solve 2.8 = 6 + 4Sin(A) And t = A ÷ π RADIANS! Home

5. Oil Pump method D Solve 2.8 = 6 + 4Sin(πt) -0.8 = Sin(πt) t = 1 + 0.2951 t = 1.295 min (πt) = Sin -1 -0.8 The height the end of the pump arm is above the ground is given by the equation H = 6 + 4Sin(πt) where t = time in minutes And H is the vertical height in metres When is the height first 2.8 metres above the ground? Height ‘H’ -3.2 = 4Sin(πt) Sketch the graph πt = -0.927 Below 0 so next highest solution? Length of 1 cycle is 2 π ÷ π = 2 Midpoint = 1 t = 0.2951 RADIANS! Home