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March 4, 2015

March 4, 2015

Posted by **Christina** on Tuesday, August 14, 2012 at 9:09pm.

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

- Math -
**Reiny**, Tuesday, August 14, 2012 at 11:05pmdy/dx = -2cos(x - π/3)

at a max/min , dy/dx = 0

-2cos(x-π/3) = 0

cos(x-π/3) = 0

I know that cos π/2 = 0 or cos 3π/2 = 0

so x - π/3 = π/2 or x - π/3 = 3π/2

x = 5π/6 or x = 11π/6 , (150° or 330°)

when x = 5π/6 , y = -2sin(π/2) = -2

when x = 11π/6 , y = -2sin(3π/2) = +2

so the function has a maximum value of 2 when x = 11π/3

and a minimum value of -2 when x = 5π/6

when y = 1

-2sin(x-π/3) = 1

sin(x-π/3) = -1/2

I know sin 210° = -1/2 and sin 330°=-1/2

which is 7π/6 or 11π/6

x-π/3 = 7π/6 or x-π/3=11π/6**x = 3π/2 or x = 13π/6**

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