Dark Calculator Cookie Settings

Dark Calculator uses cookie for smoother and better performance. Would you allow us to have cookies enabled on your browser?

Logo

Dark Calculator

ContactTermsProfile


Converters Constants Calculator Analytical Geometry


According to the rules of trigonometry:
$$sinx=\pm\sqrt{1-cos^2x}=\pm\frac{tanx}{\sqrt{1-tan^2x}}=\frac{1}{cosecx}=\pm\frac{1}{\sqrt{1+cot^2x}}=\pm\frac{\sqrt{sec^2x-1}}{secx}$$ $$cosx=\pm\sqrt{1-sin^2x}=\pm\frac{1}{\sqrt{1+tan^2x}}=\frac{1}{secx}=\pm\frac{cot^2x}{\sqrt{1-cot^2x}}=\pm\frac{\sqrt{cosec^2x-1}}{cosecx}$$ $$tanx=\pm\frac{sinx}{\sqrt{1-sin^2x}}=\pm\frac{\sqrt{1-cos^2x}}{cosx}=\frac{1}{cotx}=\pm\sqrt{sec^2x-1}=\pm\sqrt{\frac{1}{cosec^2x-1}}$$ $$cotx=\pm\frac{cosx}{\sqrt{1-cos^2x}}=\pm\frac{\sqrt{1-sin^2x}}{sinx}=\frac{1}{tanx}=\pm\sqrt{cosec^2x-1}=\pm\sqrt{\frac{1}{sec^2x-1}}$$ $$cosecx=\pm\frac{1}{\sqrt{1-cos^2x}}=\pm\frac{\sqrt{1-tan^2x}}{tanx}=\frac{1}{sinx}=\pm\sqrt{1+cot^2x}=\pm\frac{secx}{\sqrt{sec^2x-1}}$$ $$secx=\pm\frac{1}{\sqrt{1-sin^2x}}=\pm\frac{\sqrt{1+cot^2x}}{cotx}=\frac{1}{cosx}=\pm\sqrt{1+tan^2x}=\pm\frac{cosecx}{\sqrt{cosec^2x-1}}$$
According to the rules of inverse trigonometry:
$$sin^{-1}x=cos^{-1}\sqrt{1-x^2}=tan^{-1}\frac{x}{\sqrt{1-x^2}}=cot^{-1}\frac{\sqrt{1-x^2}}{x}=cosec^{-1}\frac{1}{x}=sec^{-1}\frac{1}{\sqrt{1-x^2}}$$ $$cos^{-1}x=sin^{-1}\sqrt{1-x^2}=cot^{-1}\frac{x}{\sqrt{1-x^2}}=tan^{-1}\frac{\sqrt{1-x^2}}{x}=sec^{-1}\frac{1}{x}=cosec^{-1}\frac{1}{1-x^2}$$ $$tan^{-1}x=sin^{-1}\frac{x}{\sqrt{1+x^2}}=cos^{-1}\frac{1}{\sqrt{1+x^2}}=cot^{-1}\frac{1}{x}=cosec^{-1}\frac{\sqrt{1+x^2}}{x}=sec^{-1}\sqrt{1+x^2}$$ $$cot^{-1}x=sin^{-1}\frac{1}{\sqrt{1+x^2}}=cos^{-1}\frac{x}{\sqrt{1+x^2}}=tan^{-1}x=cosec^{-1}\sqrt{1+x^2}=sec^{-1}\frac{\sqrt{1+x^2}}{x}$$ $$cosec^{-1}x=sin^{-1}\frac{1}{x}=cos^{-1}\frac{\sqrt{x^2-1}}{x}=tan^{-1}\frac{1}{\sqrt{x^2-1}}=cot^{-1}\sqrt{x^2-1}=sec^{-1}\frac{x}{\sqrt{x^2-1}}$$ $$sec^{-1}x=sin^{-1}\frac{\sqrt{x^2-1}}{x}=cos^{-1}\frac{1}{x}=tan^{-1}\sqrt{x^2-1}=cot^{-1}\frac{1}{\sqrt{x^2-1}}=cosec^{-1}\frac{x}{\sqrt{x^2-1}}$$

Convert among different Trigonometric Ratio to convert from each other: Sine, Cosine, Tan, Cotangent, Cosecant, Secant. Alongside, inverse trigonometric functions are also available.



Theory [Trigonometric Ratios and Inverse Trigonometric Functions]

Trigonometric ratios are the ratios between edges of a right triangle. Greek mathematician Hipparchus is regarded as the Father of Trigonometry, as he was the one who created the first Trigonometric Table. These ratios depend only on one acute angle of the right triangle, since any two right triangles with the same acute angle are similar. So, these ratios define functions of this angle that are called trigonometric functions. Explicitly, they are defined below as functions of the known angle A, where \(a\), \(b\) and \(h\) refer to the lengths of the sides in the accompanying figure:
Sine (denoted sin), defined as the ratio of the side opposite the angle to the hypotenuse.
$$\sin A=\frac {\textrm {opposite}}{\textrm {hypotenuse}}=\frac {a}{h}$$ Cosine (denoted cos), defined as the ratio of the adjacent leg (the side of the triangle joining the angle to the right angle) to the hypotenuse.
$$\cos A=\frac {\textrm {adjacent}}{\textrm {hypotenuse}}=\frac {b}{h}$$ Tangent (denoted tan), defined as the ratio of the opposite leg to the adjacent leg. $$\tan A=\frac {\textrm {opposite}}{\textrm {adjacent}}=\frac {a}{b}$$ The hypotenuse is the side opposite to the \(90^{\circ}\) angle in a right triangle; it is the longest side of the triangle and one of the two sides adjacent to angle A. The adjacent leg is the other side that is adjacent to angle A. The opposite side is the side that is opposite to angle A. The terms perpendicular and base are sometimes used for the opposite and adjacent sides respectively. The reciprocals of these ratios are named the cosecant (csc), secant (sec), and cotangent (cot), respectively: $$\csc A=\frac {\textrm {hypotenuse}}{\textrm {opposite}}=\frac {h}{a}$$ $$\sec A=\frac {\textrm {hypotenus}}{\textrm {adjacent}}=\frac {h}{b}$$ $$\cot A=\frac {\textrm {adjacent}}{\textrm {opposite}}=\frac {b}{a}$$ The cosine, cotangent, and cosecant are so named because they are respectively the sine, tangent, and secant of the complementary angle abbreviated to "co-".

Have functions in your mind that is not in our site? Contact Us.
   
All rights reserved by the publisher.

The website is still under development and currently in its beta version. Any kind of suggestions or feedback would be highly appreciated.

The website has been developed by:
MRK Studio
MRK Studio
About Contact Terms
Tour
Cookie Policy
Privacy Policy
MRK Studio is a leading software development company, that has been building websites, applications, softwares and creating scripts since 2023. It searches for enthausiastic programmers that would help them excel themselves for a galore growth both for the company and the individuals.
Address: Mohakhali, Dhaka-1212, Bangladesh.
Copyright: 2023-