define the modlus function for trignometric sin and cosine functions

Question

explain how the trigonometric functions change when modulus function is applied?

Answer 1

If by modulus you mean y=|sin(x)|, for example, then the sinusoidal wave appearance changes to an infinite series of "humps" along the x-axis, because the lower half of the wave sits above the axis instead of below it.

If you mean y=sin(|x|), for example, the sinusoidal wave for positive x is reflected in the y-axis for negative x. However, y=cos(|x|) is unaffected because cos(x)=cos(-x). The negative part is a natural reflection of the positive part.