Table of Contents
All Trigonometry Formulas List
Most Trigonometry formulas revolve around ratios and extremely handy to solve complex problems in Trigonometry. If you want to appear for any competitive exams after your school then hands-on knowledge of different Trigonometry formulas is essential. The basic of any Trigonometry formula is a Trigonometry Identity. So, you must be curious to know about Trigonometric identities, let us discuss the same in the next section.
Periodicity Trigonometry Formulas |
|
Co-function Trigonometry Formulas |
|
Sum/Difference Trigonometry Formulas |
|
Double Angle Trigonometry Formulas |
|
Half Angle Trigonometry Formulas |
|
Product Trigonometry Formulas |
|
Sum to Product Trigonometry Formulas |
|
Pythagorean Trigonometry Formulas |
|
Pythagorean in Radical Form of Trigonometry Formulas |
|
Odd-Even Trigonometry Formulas |
|
Ratio or Quotient Identities are given as Trigonometry Formulas |
|
Product-to-Sum Trigonometry Formulas |
|
Sum-to-Product Trigonometry Formulas |
|
Video of All Trigonometry Formulas
Trigonometric Values of Special Angles
Degree | sin | cos | tan | cot | sec | cosec |
0∘ | 0 | 1 | 0 | Not Defined | 1 | Not Defined |
30∘ | \[\frac{1}{2}\] | \[\frac{√3}{2}\] | \[\frac{1}{√3}\] | √3 | \[\frac{2}{√3}\] | 2 |
45∘ | \[\frac{1}{√2}\] | \[\frac{1}{√2}\] | 1 | 1 | √2 | √2 |
60∘ | \[\frac{√3}{2}\] | \[\frac{1}{2}\] | √3 | \[\frac{1}{√3}\] | 2 | \[\frac{2}{√3}\] |
90∘ | 1 | 0 | Not Defined | 0 | Not Defined | 1 |
What is Trigonometry?
In mathematics, Trigonometry shows the relationship between multiple sides and angles of a triangle. Trigonometry is used throughout the geometry where shapes are broken down into a collection of triangles. Basically, Trigonometry is the study of triangles, angles, and different dimensions. Although the definition may sound simpler yet it is vital for modern engineering, complex mathematics study, architecture, logarithms, calculus, and other fields. The word Trigonometry was derived from the Greek words triangle (trigōnon) and measure (matron) during the 16th century. So, this is not a new concept but into the existence of centuries and played an important role in the discovery of various mathematical and scientific theories. One of the biggest benefits of this mathematic technique was realized by the astronautical science and Indian astronomers.Trigonometric Identities
Trigonometry identities are Trigonometric functions of one or more angles where equality is defined for both sides. The identities are used to solve any complex Trigonometric equations or expressions. One of the most popular applications of Trigonometric identities is the integration of non-trigonometric functions.
\(\sin \theta = \frac{Opposite}{Hypotenuse}\)
\(\sec \theta = \frac{Hypotenuse}{Adjacent}\)
\(\cos\theta = \frac{Adjacent}{Hypotenuse}\)
\(\tan \theta =\frac{Opposite}{Adjacent}\)
\(csc \theta = \frac{Hypotenuse}{Opposite}\)
\(cot \theta = \frac{Adjacent}{Opposite}\)
The Reciprocal Identities are given as:
\(cosec\theta =\frac{1}{\sin\theta }\)
\(sec\theta =\frac{1}{\cos\theta }\)
\(cot\theta =\frac{1}{\tan\theta }\)
\(sin\theta =\frac{1}{csc\theta }\)
\(cos\theta =\frac{1}{\sec\theta }\)
\(tan\theta =\frac{1}{cot\theta }\)