a. Express 12 sin x + 5 cos x in the form R sin (x + ), where R and are constants, R >

a. Express 12 sin x + 5 cos x in the form R sin (x + α), where R and α are constants, R > 0 and 0

A runner’s speed, v in m/s, in an endurance race can be modelled by the equation.

where x is the time in minutes since the beginning of the race.

b. Find the minimum value of v.

c. Find the time into the race when this speed occurs.

50 2x 2x 12 sin () + 5 cos () 5 5 v(x) = - 0x300