Why dont sin and phase shifted cosine overlap?

1. Why is the cosine wave said to be a sine wave with a phase lead of 90?
2. What does phase shift mean for cosine?
3. What is the horizontal shift of a sin function?

Why is the cosine wave said to be a sine wave with a phase lead of 90?

When you look at a cosine and sine wave the cosine leads by 90 degrees because, for this example cos(0)=1 while sin(0)=0. sine will not reach a value of 1 until a 1/4 of the cycle has occurred which is 90 degrees (360/4).

What does phase shift mean for cosine?

Phase Shift is a shift when the graph of the sine function and cosine function is shifted left or right from their usual position or we can say that in phase shift the function is shifted horizontally how far from the usual position. Generally, functions are shifted (π/2) from the usual position.

What is the horizontal shift of a sin function?

Such translations also occur when dealing with trigonometric functions, with a horizontal translation, or horizontal shift, being one of the most prominent transformations. The graphs of sine and cosine are the same when sine is shifted left by 90º or. radians. Such a shifting is referred to as a horizontal shift.