F4 math problem

圖片參考：http://hk.yimg.com/i/icon/16/1.gif
Consider y = k sin(θ - 20°) where 0° ≦θ ≦360° and k ＞0.
The maximum value of y is 4.


(a) Find the value of k.
since
-1 <= sin(θ - 20) <= 1
-k <= ksin(θ - 20) <= 4
k = 4

(b) Find the minimum value of y and the corresponding value of θ.
refer to above deduction
minimum is -4
when y = -4
-4 = 4sin(θ - 20)
sin(θ - 20) = -1
sin(θ - 20) = sin270
θ - 20 = 270
θ = 290
always remember
-1 <= sinx <= 1
圖片參考：http://hk.yimg.com/i/icon/16/4.gif

The answer of (a) is:
as the range of sin (θ - 20°) = -1 to 1
Therefore if we take the maximum value, sin (θ - 20°) should take the value of 1.
Therefore k x 1 = 4
k = 4

The answer of (b) is:
the minimum of y=-4
since the min value for sin(θ - 20°)=-1
so ksin(θ - 20°)=4sin(θ - 20°)=4*-1=-4

sin(θ - 20°)=-1
θ - 20°=270°
θ=290°

a)
k =4
since the max value for sin(θ - 20°) =1

b)
min value of y=-4
since the min value for sin(θ - 20°)=-1
so ksin(θ - 20°)=4sin(θ - 20°)=4*-1=-4

sin(θ - 20°)=-1
θ - 20°=270°
θ=290°

(a) as the range of sin (θ - 20°) = -1 to 1
Therefore if we take the maximum value, sin (θ - 20°) should take the value of 1.
Therefore k x 1 = 4
k = 4

(b) the minimum value of y is -4 when θ = 270°