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.

Contents

## What is sin in geometry?

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.

## What is sin a equal to?

Always, always, the sine of an angle is equal to the opposite side divided by the hypotenuse (opp/hyp in the diagram). The cosine is equal to the adjacent side divided by the hypotenuse (adj/hyp).

## Why is sin the Y value?

So z = sin(θ) which means that the length of the line between the x- axis and the point on the circle is sin(θ). This is why the y-axis is called the “sine” – that’s what it represents on a triangle.

## Is Sin Cos Tan?

The tangent of x is defined to be its sine divided by its cosine: tan x = sin x cos x. The secant of x is 1 divided by the cosine of x: sec x = 1 cos x, and the cosecant of x is defined to be 1 divided by the sine of x: csc x = 1 sin x.

## How do you write cosecant?

Cosecant ( csc ) – Trigonometry function In a right triangle, the cosecant of an angle is the length of the hypotenuse divided by the length of the opposite side. In a formula, it is abbreviated to just ‘csc’.

## Is YX a tan?

The unit circle definition is tan (theta)=y/x or tan(theta)=sin(theta)/cos(theta). The tangent function is negative whenever sine or cosine, but not both, are negative: the second and fourth quadrants. Tangent is also equal to the slope of the terminal side. Like we have for the sine and cosine.

## How do you convert Arcsin to sin?

The inverse sine function, arcsine, will take the ratio of the opposite/hypotenuse (x) and return the angle, θ. So, knowing that, for our triangle, arcsin(x) = θ we can also write that: Sine: sin(arcsin(x)) = x. Cosine: cos (arcsin(x)) = √(1-x²)

## What is Cosec in math?

Cosecant is one of the six trigonometric ratios which is also denoted as cosec or csc. The cosecant formula is given by the length of the hypotenuse divided by the length of the opposite side in a right triangle.