# What is the reduction formula in trigonometry?

## What is the reduction formula in trigonometry?

Key Equations

Double-angle formulas sin(2θ)=2sin θ cos θcos(2θ)=cos2θ−sin2θ=1−2sin2θ=2cos2θ−1tan(2θ)=2tan θ1−tan2θ
Reduction formulas sin2θ=1−cos(2θ)2cos2θ=1+cos(2θ)2tan2θ=1−cos(2θ)1+cos(2θ)
Half-angle formulas sin α2=±√1−cos α2cos α2=±√1+cos α2tan α2=±√1−cos α1+cos α=sin α1+cos α=1−cos αsin α

What is a general solution in trigonometry?

Solutions for Trigonometric Equations. are solutions of the given equation. Hence, the general solution for sin x = 0 will be, x = nπ, where n∈I. Similarly, general solution for cos x = 0 will be x = (2n+1)π/2, n∈I, as cos x has a value equal to 0 at π/2, 3π/2, 5π/2, -7π/2, -11π/2 etc.

### What is the formula of sin 180 Theta?

It is also called trigonometric ratio. If theta is an angle in a right-angled triangle, then sine theta is equal to the ratio of perpendicular and hypotenuse of the right triangle. To be noted the value of sin 0 is also equal to 0….Sine Value Table.

Sine Degree Sine Function Values
sin 150 1/2
sin 180 0
sin 270 -1
sin 360 0

When can you use reduction formula?

A reduction formula is one that enables us to solve an integral problem by reducing it to a problem of solving an easier integral problem, and then reducing that to the problem of solving an easier problem, and so on.

## What is the general solution of an equation?

The general solution includes all possible solutions and typically includes arbitrary constants (in the case of an ODE) or arbitrary functions (in the case of a PDE.) A solution without arbitrary constants/functions is called a particular solution.

What are the basic formula of trigonometry?

The trigonometry formulas for trigonometry ratios when the angles are in addition are given as, sin(x + y) = sin(x)cos(y) + cos(x)sin(y) cos(x + y) = cos(x)cos(y) – sin(x)sin(y) tan(x + y) = (tan x + tan y)/(1 – tan x • tan y)

### When to use a reduction formula in trigonometry?

Reduction formulae 180° ± θ, 360° – θ, 90° ± θ  180° and 360° lie on the x-axis. If one works off the x-axis with angles such as 180° – θ, 180° + θ, 360° – θ or – θ, the ratio is unchanged.  When reducing ratios of angles (90 ), the ratios change to the Co-functions.

Which is the correct formula for a trigonometric equation?

It is a branch of Mathematics that deals with the relationships between the lengths and angles of the sides of triangles. Trigonometric equation is an equation involving one or more trigonometric ratios of unknown angles. It is expressed as ratios of sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), cosecant (cosec) angles.

## What is the reduction formula for 180° and 360°?

Reduction formulae 180° ± θ, 360° – θ, 90° ± θ  180° and 360° lie on the x-axis. If one works off the x-axis with angles such as 180° – θ, 180° + θ, 360° – θ or – θ, the ratio is unchanged.

When do you need to rewrite a trigonometric equation?

When solving some trigonometric equations, it becomes necessary to rewrite the equation first using trigonometric identities. One of the most common is the Pythagorean identity, 22    sin ( ) cos ( ) 1 which allows you to rewrite )2 sin ( in terms of )2 cos ( or vice versa, 22 22 sin ( ) 1 cos ( ) cos ( ) 1 sin ( )      