Al-Huda Science Academy has created Math Class 11 Chapter 12 Formulas for better trigonometric ratios understanding.
Math Class 11 Chapter 12 Formulas
THE DISTANCE FORMULA
Let A(x1, y1) and B(x2, y2) be any two points on the plane, then
|AB| = √(x2− x1)2+ (y2− y1)2 is called as the distance formula. Where |AB| indicates the distance between A and B.
THE LAW OF SINES
The measures of sides are proportional to the sines of the measures of opposite angles.
Note: Suppose that according to the above figure if a/sinα = 10, then b/sinβ and c/sinγ are also equal to 10.
THE LAWS OF COSINES
a2 = b2 + c2 – 2bcCosα
b2 = c2 + a2 – 2caCosβ
c2 = a2 + b2 – 2abCosγ
The laws of cosines can also be written as follows in order to measure the angles
THE LAWS OF TANGENTS
NOTE: – The law of Sines and the Laws of Cosines and Tangents are used to find the remaining elements of a triangle.
Half Angle Formulae In Terms Of The Lengths Of The Sides Of A Triangle
Tangent formulas can also be written as
Note: These formulas are used to find the angles when three sides of triangle are given.
Area Of A Triangle And Its Formulas In Various Cases
Area of a triangle: – The area of a triangle is the number of square units insidethat triangle. It is denoted by filled triangle i.e., “∆”.
The general formula for measuring it is:
Area = Where, “b” is the base and “a” is the corresponding altitude of the triangle.
In trigonometry area of triangle is being measured by various ways and formulas depending upon the given conditions. At this stage there are three main cases based on given data.
CASE I: –
When the measures of two sides and the measure of the included angle are known.
CASE II: –
When the measures of two angles and the measure of one side are given.
CASE III: –
When the measures of all three sides are known.
where “s” semi-perimeter
Note: This is also known as Heron’s Formula