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# How do you explain sine?

## How do you explain sine?

The sine of one of the angles of a right triangle (often abbreviated “sin”) is the ratio of the length of the side of the triangle opposite the angle to the length of the triangle’s hypotenuse….In other words:

1. SOH → sin = “opposite” / “hypotenuse”
2. CAH → cos = “adjacent” / “hypotenuse”
3. TOA → tan = “opposite” / “adjacent”

How is sine calculated?

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 sine θ?

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 is sine law?

law of sines, Principle of trigonometry stating that the lengths of the sides of any triangle are proportional to the sines of the opposite angles. That is, when a, b, and c are the sides and A, B, and C are the opposite angles.

Why is sine important?

As we learned, sine is one of the main trigonometric functions and is defined as the ratio of the side of the angle opposite the angle divided by the hypotenuse. It’s important for finding distances or height and can also be used to find angle measures, which are measured in radians.

Why sine is 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 is value of sine?

The value of sine varies as the angle between the base and hypotenuse of a right-angled triangles changes. The commonly used values of the sine are: sin 0 = 0, sin π/6 = 1/2, sin π/4 = 1/√2, sin π/3 = √3/2, and sin π/2 = 1. We can determine these values using the sine formula given by, sin x = Perpendicular/Hypotenuse.

What is sin equal to?

The sine of an angle is equal to the ratio of the opposite side to the hypotenuse whereas the cosine of an angle is equal to the ratio of the adjacent side to the hypotenuse.

What is sin value?

Answer: The value of sin and cos infinity lies between -1 to 1. There are no exact values defined for them.

## Who discovered law of sine?

According to Ubiratàn D’Ambrosio and Helaine Selin, the spherical law of sines was discovered in the 10th century. It is variously attributed to Abu-Mahmud Khojandi, Abu al-Wafa’ Buzjani, Nasir al-Din al-Tusi and Abu Nasr Mansur.

What is sine used for in real life?

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