Question

For the function -2sin(x-(pi/3)) between x = 0 and x = 2 : (6 marks)

For what value(s) of x does y have its maximum value?
For what value(s) of x does y have its minimum value?
For what value(s) of x does y=1?

Answer 1

you know that sin(x) has maximum value at x = pi/2. So, x - pi/3 = pi/2, or x = 5pi/6. However, that is not in the interval [0,2].

So, try x - pi/3 = -3pi/2. x = -7pi/6.

So, y does not achieve its maximum possible value over x in [0,2]. So, the max achieved in [0,2] occurs when x=2, and y = 2sin(2 - pi/3)

Similarly for the others.