How do you stretch a sine graph?

How do you stretch a sine graph?

To horizontally stretch the sine function by a factor of c, the function must be altered this way: y = f (x) = sin(cx) . Such an alteration changes the period of the function.

What is phase shift in trig?

When we move our sine or cosine function left or right along the x-axis, we are creating a Horizontal Shift or Horizontal Translation. In trigonometry, this Horizontal shift is most commonly referred to as the Phase Shift. As Khan Academy states, a phase shift is any change that occurs in the phase of one quantity.

How do you shift a sine graph to the right?

By adding or subtracting a number from the angle (variable) in a sine equation, you can move the curve to the left or right of its usual position. A shift, or translation, of 90 degrees can change the sine curve to the cosine curve.

How do you know if it is a horizontal stretch or compression?

If the constant is between 0 and 1, we get a horizontal stretch; if the constant is greater than 1, we get a horizontal compression of the function. Given a function y=f(x) y = f ( x ) , the form y=f(bx) y = f ( b x ) results in a horizontal stretch or compression.

How do you shift a cosine graph to the right?

Move the graph vertically….For example,

  1. f(x) = sin(x – 3) moves the parent graph of y = sin x to the right by 3.
  2. g(x) = cos(x + 2) moves the parent graph of y = cos x to the left by 2.
  3. k(x) = sinx + 4 moves the parent graph of y = sin x up 4.
  4. p(x) = cosx – 4 moves the parent graph of y = cos x down 4.

How do you graph trigonometric functions?

Just watch where your function goes to + ∞ and where to − ∞. Remember to help yourself with the unit circle. All you need for the graphs of trigonometric functions are there; you just need to practice concluding from it. And the final look of the function tangent: Cotangent is a function derived from functions sine and cosine.

How many trig functions are there?

It is here just to remind you of the graphs of the six trig functions as well as a couple of nice properties about trig functions. Before jumping into the problems remember we saw in the Trig Function Evaluation section that trig functions are examples of periodic functions.

What are the three basic trigonometry ratios?

Graphs of Trigonometric Functions Sine, Cosine and tangent are the three important trigonometry ratios, based on which functions are defined. Below are the graphs of the three trigonometry functions sin x, cos x, and tan x.

Can trigonometric functions be altered?

Like any other functions, trigonometric functions can also be altered, they can be translated and be more “dense” or “rare”. Let’s break down this function.