Trigonometric Functions Identities
There are various identities that are related to the trigonometric function these identities link different trigonometric function with each other and are very useful in solving various trigonometric problems. Various trigonometry identities used by us are,
Reciprocal Identities
Reciprocal Identities of the trigonometric functions include,
- cosec θ = 1/sin θ
- sec θ = 1/cos θ
- cot θ = 1/tan θ
- sin θ = 1/cosec θ
- cos θ = 1/sec θ
- tan θ = 1/cot θ
Pythagorean Identities
Pythagorean Identities of the trigonometric functions include,
- sin2θ + cos2θ = 1
- 1 + tan2θ = sec2θ
- 1 + cot2θ = cosec2θ
Complementary Angles Identities
Complementary Angles Identities of the trigonometric functions include,
- sin (90° – θ) = cos θ
- cos (90° – θ) = sin θ
- tan (90° – θ) = cot θ
- cot ( 90° – θ) = tan θ
- sec (90° – θ) = cosec θ
- cosec (90° – θ) = sec θ
Supplementary Angles Identities
Supplementary Angles Identities of the trigonometric functions include,
- sin (180°- θ) = sinθ
- cos (180°- θ) = -cos θ
- cosec (180°- θ) = cosec θ
- sec (180°- θ)= -sec θ
- tan (180°- θ) = -tan θ
- cot (180°- θ) = -cot θ
Even and Odd Trigonometric Functions
Among the six trigonometric functions Cos and Sec functions are even functions and the rest four function Sin, Tan, Cosec, and Cot are odd function, i.e.
- sin(-x) = -sin x
- cos(-x) = cos x
- tan(-x) = – tan x
- cot(-x) = -cot x
- csc(-x) = -csc x
- sec(-x) = sec x
Periodic Trigonometric Functions
Trigonometric Functions are periodic functions and the period of trigonometric function are added below,
- sin(x+2nπ) = sin x
- cos(x+2nπ) = cos x
- tan(x+nπ) = tan x
- cot(x+nπ) = cot x
- csc(x+2nπ) = csc x
- sec(x+2nπ) = sec x
Trigonometric Functions
Trigonometric Functions, often simply called trig functions, are mathematical functions that relate the angles of a right triangle to the ratios of the lengths of its sides. These Trigonometric functions are fundamental in mathematics for units like Calculus and Geometry and have wide-ranging applications in science, engineering, and various other fields.
In this article, we will in detail about trigonometric functions, their domain and range, and other related facts.
Table of Content
- What are Trigonometric Functions?
- Six Trigonometric Functions
- Trigonometric Functions Formulas
- Trigonometric Functions Values
- Trigonometric Functions in Four(4) Quadrants
- Graphs of Trigonometric Functions
- Trigonometric Functions Identities
- Domain and Range of Trigonometric Functions
- Derivative of Trigonometric Functions
- Integration of Trigonometric Functions
- Inverse Trigonometric Functions