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 . No matter the size of the triangle, the values of sin(θ) and cos(θ) are the same for a given θ, as illustrated below.

## What is sin theta?

In the context of a right angle, the sine function, written as sinθ is equal to the division of the opposite side of the reference angle (θ) by the hypotenuse, or long side, of the triangle. sinθ=oppositehypotenuse.

## What is value of sin theta?

θsin θtan θ0°0090°1undefined180°00270°−1undefined1 more row

## What is sin θ π 2?

Sine (theta+pi/2) is equal to cosine.

## What is sin equal to in math?

Sine (sin) function - Trigonometry. In a right triangle, the sine of an angle is the length of the opposite side divided by the length of the hypotenuse. In any right triangle, the sine of an angle x is the length of the opposite side (O) divided by the length of the hypotenuse (H).

## What is the maximum value of sin theta?

1 Therefore, the maximum value of sinθ is 1, we get this value when θ=90o .

## What is the reciprocal of sin theta?

The reciprocal sine function is cosecant, csc(theta)=1/sin(theta). The reciprocal tangent function is cotangent, expressed two ways: cot(theta)=1/tan(theta) or cot(theta)=cos(theta)/sin(theta).

## Does sin pi equal zero?

In trigonometry, we use pi (π) for 180 degrees to represent the angle in radians. Hence, sin π is equal to sin 180 or sin π = 0.

## What is pi 2 angle?

The circumference of the entire circle is 2π, so it follows that 360° equals 2π radians. Hence, 1° equals π/180 radians.

## Where is sin theta used?

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 .

sin3θ=sin(θ+2θ)=sinθcos(2θ)+sin(2θ)cosθ.

## Is sin 1 the same as csc?

So the reciprocal of the sine function is called the cosecant and is equal to the hypotenuse / opposite. It is important to note that there is a big difference between the reciprocal value csc θ and sin-1x. The cosecant function means 1/sin θ, while the second involves finding an angle whose sine is x.

## Why does sin pi?

In trigonometry, we use pi (π) for 180 degrees to represent the angle in radians. Hence, sin π is equal to sin 180 or sin π = 0.