# Characteristics of sine function

## What defines a sine function?

In trigonometry, the sine function can be defined as

**the ratio of the length of the opposite side to that of the hypotenuse in a right-angled triangle**. The sine function is used to find the unknown angle or sides of a right triangle.## What are the 5 key points of sine?

The key points for sine are

**(0, 0), (π2,1), (π, 0), (3π2,−1), and (2π, 0)**. Graph the key points and sketch the sine curve through the points. Then continue the pattern both positive and negative.## What are the characteristics of a trigonometric function?

The properties of the 6 trigonometric functions: sin (x), cos (x), tan(x), cot (x), sec (x) and csc (x) are discussed. These include the

**graph, domain, range, asymptotes (if any), symmetry, x and y intercepts and maximum and minimum points**.## What is the argument of a sine function?

The classical definition of the sine function for real arguments is: “

**the sine of an angle in a right‐angle triangle is the ratio of the length of the opposite leg to the length of the hypotenuse**.” This description of is valid for when the triangle is nondegenerate.## How do you find the critical points of a sine function?

## What is the five point pattern for the sine function when a 0?

The five-point pattern for the sine function when a > 0 is

**zero-max-zero-min-zero**, as shown on the graph.## Why is it called sine?

In trigonometry, the name “sine”

**comes through Latin from a Sanskrit word meaning “chord”**. In the picture of a unit circle below, AB has length sinθ and this is half a chord of the circle. The co-functions are functions of complementary angles: cosθ = sin(π/2 − θ), cotθ = tan(π/2 − θ), and cscθ = sec(π/2 − θ).## What are the parameters of a sine wave?

**the parameter A — called the amplitude,**

**the parameter p — called the period,**

**the parameter d called the shift, and**.

**the parameter B — called the center**.

## 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 are the values of sin?

Sine Definition In Terms of Sin 0

Sine Degrees/Radians | Values |
---|---|

Sin 0^{0} | 0 |

Sin 30^{0} or Sin π/6 | 1/2 |

Sin 45^{0} or Sin π/4 | 1 / 2 |

Sin 60^{0} or Sin π/3 | 3 / 2 |

## What are the five points that are used to plot the cosine wave?

The values of cos x correspond to the x-values, so those key points are

**(angle, x-value) or (0,1), (π/2, 0), (π, -1), (3π/2, 0), (2π, 1)**.## How do you find the key points on a graph?

## What is the formula for sin?

The sine of an angle of a right-angled triangle is the ratio of its perpendicular (that is opposite to the angle) to the hypotenuse. The sin formula is given as:

**sin θ = Perpendicular / Hypotenuse**. sin(θ + 2nπ) = sin θ for every θ## What is the pattern of sine graph?

Summary. 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 .## How do you describe a sine graph?

To graph the sine function, we

**mark the angle along the horizontal x axis, and for each angle, we put the sine of that angle on the vertical y-axis**. The result, as seen above, is a smooth curve that varies from +1 to -1. Curves that follow this shape are called ‘sinusoidal’ after the name of the sine function.## What is frequency of sine wave?

A frequency of

**1000Hz, or 1 kHz**, means that the sine wave goes through 1000 complete cycles in 1 s. If we are considering audible sound waves then the human ear has a frequency range of about 20Hz-20kHz. The electrical mains frequency in Europe is 50Hz and 60Hz in America.## What is amplitude of sine wave?

The amplitude of the sine and cosine functions is

**the vertical distance between the sinusoidal axis and the maximum or minimum value of the function**. In relation to sound waves, amplitude is a measure of how loud something is.## What is the wavelength of a sine wave?

The wavelength can be measured as the distance from crest to crest or from trough to trough. In fact, the wavelength of a wave can be measured as the distance from a point on a wave to the corresponding point on the next cycle of the wave. In a sine wave, the wavelength is

**the distance between peaks**.## What are the three characteristics of a sine wave?

Sinusoidal Amplitude, Frequency, and Phase

The three characteristics that separate one sinusoid from another are **amplitude, frequency, and phase**.

## Where are sine waves used?

Sine waves are used in

**technical analysis and trading to help identify patterns and cross-overs related to oscillators**.