The Sine function (abbreviated sin) takes an angle and gives a ratio which is based on the sides of a right triangle. If you have a right triangle, and one of the angles (not the right angle) is labeled y then sin y equals the length of the side opposite of angle y divided by the length of the hypotenuse. The hypotenuse of a right triangle is the longest side, and is always opposite of the right angle.
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y= sin 3x
y = 2 sin 3x y' = 2(sin 3x)'(3x)' y' = 2(cos 3x)(3) y' = 6 cos 3x
If x = sin θ and y = cos θ then: sin² θ + cos² θ = 1 → x² + y² = 1 → x² = 1 - y²
We have:int int (x * sin(y)) dx dyIntegrate x first:int(x)dx = 1/2 * x2 + CNow integrate sin(y):int(sin(y))dy = -cos(y) + CMultiply:-1/2 * x2 * cos(y) + C
y = sin(-x)Amplitude = 1Period = 2 pi