π

 

I don’t know whether this video should go under “Weird Videos” or “Math”.

How to Find the Maximum & Minimum Values

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)

 

Dealing with Negative Values of Sine, Cosine and Tangent

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= -y

χ=Sin^-1(y)

χ=β   (base angle, quadrant 1)

χ=180°+β, 360°-β

      (III)         (IV)

 

Since tangent is negative in the second (II) and fourth (IV) quadrant, to find the values you must subtract the base angle from 180 for the second quadrant, and then from 360 for the fourth quadrant.

Tanχ=-y

χ=180°-β, 360°-β

       (II)        (IV)

Lastly, cosine is negative in the second (II) and third (III) quadrant, therefore you must subtract the base angle from 180 for the second quadrant value and add the base angle to 180 for the value of the third quadrant.

Cosχ= -y

χ=180°-β, 180°+β

      (II)          (III)

 

Quadrants

Quadrants

Sine, Cosine, Tangent

∠A= θ

∠B = 90-θ

∵∠B+θ+90= 180

∠B+θ=180-90

∠B=90-θ

• Sinθ= a/c
• Cosθ=b/c
• Tanθ=a/b

• Sin(90-θ)= b/c
• Cos(90-θ)= a/c
• Tan(90-θ)= b/a

∴

• Sinθ = Cos(90-θ)
• Cosθ = Sin(90-θ)
• Tanθ = 1/Tan(90-θ)