Question: How Do You Tell If A Graph Is Sine Or Cosine?

In what ways are the sine and cosine graphs similar?

The graphs of sine and cosine have the same shape: a repeating “hill and valley” pattern over an interval on the horizontal axis that has a length of .

The sine and cosine functions have the same domain—the real numbers—and the same range—the interval of values ..

What does a negative sine graph look like?

The difference with a negative value of a however, is our sine curve now has a negative amplitude. In other words, our graphs are the same as when a was a positive value, but are now reflected across the x-axis. … Notice how different values of a change the amplitude of our sine curve.

What is a cosine wave?

A cosine wave is a signal waveform with a shape identical to that of a sine wave , except each point on the cosine wave occurs exactly 1/4 cycle earlier than the corresponding point on the sine wave.

What is negative sine?

The negative -θ of an angle θ is the angle with the same magnitude but measured in the opposite direction from the positive x-axis. … When a point (a,b) is reflected in the x-axis, it moves to the point (a,-b). So Q also has coordinates (cos(θ),-sin(θ)).

Is amplitude negative or positive?

Amplitudes are always positive numbers (for example: 3.5, 1, 120) and are never negative (for example: -3.5, -1, -120). Amplitudes are positive because distance can only be greater than zero or equal to zero; negative distance does not exist.

Why is sine cosine important?

Because these functions turn up a lot in nature and they also are useful tools in mathematics. The sine and cosine functions are almost the same – they are just shifted a little bit compared to each other. They come up a lot in systems that have circular motion. … The sine function is needed to describe waves.

Why is it called cosine?

Similarly the cosine can be thought of as measuring the distance from the y-axis of that same point. It is useful to note that the cosine of an angle is the same as the sine of the complement of the angle. … The word sine originally came from the latin sinus, meaning “bay” or “inlet”.

What does a sine graph look like?

Plot of Sine The Sine Function has this beautiful up-down curve (which repeats every 2π radians, or 360°). It starts at 0, heads up to 1 by π/2 radians (90°) and then heads down to −1.

What is the difference between sine and cosine?

Sine and cosine — a.k.a., sin(θ) and cos(θ) — are functions revealing the shape of a right triangle. Looking out from a vertex with angle θ, sin(θ) is the ratio of the opposite side to the hypotenuse , while cos(θ) is the ratio of the adjacent side to the hypotenuse .

What does a cos graph look like?

To graph the cosine function, we mark the angle along the horizontal x axis, and for each angle, we put the cosine of that angle on the vertical y-axis. The result, as seen above, is a smooth curve that varies from +1 to -1. … As you do so, the point on the graph moves to correspond with the angle and its cosine.

What does a negative do to a graph?

Making the input and the output of a function negative results in a rotation of the function around the origin. Here is a graph of y = f (x) and y = – f (- x). Note that if (x, y) is a point on the graph of f (x), then (- x, – y) is a point on the graph of – f (- x).