y=αSinχ+z
max=α min=-α
e.g.
y=2Sinχ+5
max=α+z max=2+5 = 7
min=-α+z min=-2+5 = 3
(this also applies to y=z-αSinχ)
If any value of sine, cosine or tangent has a negative result, you must find which quadrants sine, cosine or tangent is negative in.
Since sine is negative in the third (III) and fourth (IV) quadrant, you must add the base angle and 180 together to find the value for the third quadrant, and subtract 360 from the base angle to find the value of the fourth quadrant.
Sinχ= -yχ=Sin-1(y)χ=β (base angle, quadrant 1)χ=180°+β, 360°-β(III) (IV)
Tanχ=-yχ=180°-β, 360°-β(II) (IV)
Cosχ= -yχ=180°-β, 180°+β(II) (III)
∠A= θ
∠B = 90-θ
∵∠B+θ+90= 180
∠B+θ=180-90
∠B=90-θ
∴