# How are sine and cosine graphs used in real life?

## How are sine and cosine graphs used in real life?

In real life, sine and cosine functions can be used in space flight and polar coordinates, music, ballistic trajectories, and GPS and cell phones.

## What are sine and cosine graphs?

The basic sine and cosine functions have a period of 2π. The function sin x is odd, so its graph is symmetric about the origin. The function cos x is even, so its graph is symmetric about the y-axis. The graph of a sinusoidal function has the same general shape as a sine or cosine function.

What are the applications of sine and cosine graphs?

Sine and cosine functions can be used to model many real-life scenarios – radio waves, tides, musical tones, electrical currents.

### Why is cosine useful?

The law of cosines is useful for computing the third side of a triangle when two sides and their enclosed angle are known, and in computing the angles of a triangle if all three sides are known.

### Where is cosine used?

To solve a triangle is to find the lengths of each of its sides and all its angles. The sine rule is used when we are given either a) two angles and one side, or b) two sides and a non-included angle. The cosine rule is used when we are given either a) three sides or b) two sides and the included angle.

Where do cos graphs start?

A standard cosine starts at the highest value, and this graph starts at the lowest value, so we need to incorporate a vertical reflection.

#### What is a cosine graph?

The cosine graph or the cos graph is an up-down graph just like the sine graph. The only difference between the sine graph and the cos graph is that sine graph starts from 0 while the cos graph starts from 90 (or π/2). The cos graph given below starts from 1 and falls till -1 and then starts rising again.

#### How do you graph a cosine graph?

Here are the steps:

1. Find the values for domain and range. Like with sine graphs, the domain of cosine is all real numbers, and its range is.
2. Calculate the graph’s x-intercepts.
3. Calculate the graph’s maximum and minimum points.
4. Sketch the graph of the function.

What are the top 3 careers that use trig functions?

Trigonometry spreads its applications into various fields such as architects, surveyors, astronauts, physicists, engineers and even crime scene investigators.

## How to graph the sine and cosine functions?

You can graph sine and cosine functions by understanding their period and amplitude. Sine and cosine graphs are related to the graph of the tangent function, though the graphs look very different. How to graph the sine and cosine function on the coordinate plane using the unit circle?

## What is the difference between standard cosine and sine?

Let’s use a cosine function because it starts at the highest or lowest value, while a sine function starts at the middle value. A standard cosine starts at the highest value, and this graph starts at the lowest value, so we need to incorporate a vertical reflection.

What is the domain of Sine and cosine?

Even symmetry of the cosine function The sine and cosine functions have several distinct characteristics: They are periodic functions with a period of 2π. The domain of each function is (−∞,∞) ( − ∞, ∞) and the range is [−1,1] [ − 1, 1]. x is symmetric about the origin, because it is an odd function.

### What does the gray portion of the sine curve indicate?

The gray portion of the graph indicates that the basic sine curve repeats indefinitely in the positive and negative directions. The graph of the cosine function is shown in Figure 4.48. Recall from Section 4.2 that the domain of the sine and cosine functions is the set of all real numbers.

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