Table of Contents

## Sine And Its Function

A sine wave is a mathematical curve that describes a smooth oscillation. It is named after the function sine, which produces it. The sine wave is a continuous function, meaning that it has no breaks or discontinuities in its graph.

The sine wave is also a periodic function, meaning that its graph repeats itself after a certain interval of time. The period of a sine wave is the amount of time it takes for the wave to complete one full cycle.

The amplitude of a sine wave is the maximum height of the wave. The amplitude is measured from the baseline (zero) to the peak of the wave.

The wavelength of a sine wave is the distance between two consecutive peaks of the wave.

The frequency of a sine wave is the number of times the wave repeats itself per second. Frequency is measured in hertz (Hz).

## Sine Function Formula

The sine function is a mathematical function that is used to calculate the length of a side of a right triangle, or the angle between two lines. The sine function is represented by the letter “s” and is abbreviated as sin(). The sine function is also used to calculate the height of a triangle, or the length of a chord.

## Sine Identities

The sine identities are a set of mathematical relationships between the sine function and other trigonometric functions. There are six identities in all, each of which can be proved using basic algebra.

The first identity states that the sine of an angle is equal to the cosine of the complementary angle. The second identity states that the sine of an angle is equal to the product of the cosine and the hypotenuse. The third identity states that the cosine of an angle is equal to the product of the sine and the hypotenuse. The fourth identity states that the tangent of an angle is equal to the ratio of the sine and the cosine. The fifth identity states that the cotangent of an angle is equal to the ratio of the cosine and the tangent. The sixth and final identity states that the secant of an angle is equal to the ratio of the cosine and the secant.

## Trigonometry Law of Sines

The law of sines states that in any triangle, the sine of a given angle is equal to the opposite side divided by the hypotenuse.

## Sine Function Graph

The graph of the sine function is a smooth curve that oscillates between the values -1 and 1.

## Sine Calculus

The sine calculus is a branch of mathematics that deals with the properties of sine curves. It was developed in the early 19th century by French mathematician Jules Henri Poincaré.

## Solved Example:

The average of five numbers is 34.

What is the fifth number?

The fifth number is 42.

### Sine Function Formula

The diagram below shows that Sin α = BC/AB.

Hence, we can write the formula as:

Sin α = a/h

Image will be uploaded soon

Given below is the sine table from 0 degree to 360 degree with their respective values.