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Math Calculators ▶ Trigonometry Calculator

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**Table of Content**

Try this trigonometry calculator that lets you calculate the trigonometric angle functions (sin, cos, tan, sec, csc, tan) in either degrees or radians. Not only this but the sohcahtoa calculator with steps will apply this particular mnemonics to determine the trigonometric angle ratios accurately, thereby representing the graph as well.

Letâ€™s move on to the article below and learn how to find angle function values by utilising this trigonometry calculator or manually.

Stay focused!

**The study of three angles of the triangle is called trigonometry.**

Picâ€¦

Our free trig calculator triangle also goes for determining all the interconnected angle ratios in a couple of moments.

The following are the standard trigonometric function ratios that can also be computed for any angle by using our online find trigonometric ratios calculator:

The ratio of perpendicular to the hypotenuse length is termed sine.

**Formula:**

**Sine = Perpendicular/Hypotenuse**

The exact value of the sine angles can be computed using this trigonometry calculator triangle.

In trigonometry, the ratio of the base to the hypotenuse of the triangle is known as the cosine function that could be understood in detail by a free cosine calculator.

**Formula:**

**Cosine = Base/Hypotenuse**

The ratio of perpendicular and base of the triangle is known as the tangent function.

**Formula:**

**Tangent = Perpendicular/Base**

Secant is exactly opposite of sine. In other words, it corresponds to the ratio of hypotenuse and perpendicular.

**Formula:**

**Secant = Hypotenuse/Perpendicular**

Like sine and secant, cosecant is the ratio opposite to that of the cosine. Simply put, the ratio of hypotenuse to the base of the triangle is known as the cosecant.

**Formula:**

**Cosecant = Hypotenuse/Base**

The ratio of base to the perpendicular of a triangle is known as cotangent function.

**Formula:**

**Cotangent = Base/Perpendicular**

Simply put, the inverse of trigonometric functions are inverse trigonometric functions. Among these include:

It is the inverse of sine function.

**Formula:**

Arcsin = sin^{-1}x

The inverse of the cosine function is termed as arccos.

**Formula:**

Arccos = cos^{-1}x

The exact opposite of the tangent function is known as the arctan function.

**Formula:**

Arctan = tan^{-1}x

The reciprocal of cotangent function is called arccotangent function.

**Formula:**

Arccot = cot^{-1}x

This particular function is actually the inverse of secant function.

**Formula:**

Arcsec = sec^{-1}x

The inverse of cosecant function is arccosecant function.

**Formula:**

Arccosecant = cosec^{-1}x

All of these trig functions yield different degrees or radians values for different measures of azimuthals. And it is pretty hard to calculate for each value separately. But this is where our free right triangle trigonometry calculator comes to aid. So use this calculator and start solving for different angles.

Function | Description | Relationship | |

using radians | using degrees | ||

sine | opposite
/hypotenuse |
$$ {\displaystyle \sin \theta =\cos \left({\frac {\pi }{2}}-\theta \right)={\frac {1}{\csc \theta }}} $$ | $$ {\displaystyle \sin x=\cos \left(90^{\circ }-x\right)={\frac {1}{\csc x}}} $$ |

cosine | adjacent
/hypotenuse |
$$ {\displaystyle \cos \theta =\sin \left({\frac {\pi }{2}}-\theta \right)={\frac {1}{\sec \theta }}\,} $$ | $$ {\displaystyle \cos x=\sin \left(90^{\circ }-x\right)={\frac {1}{\sec x}}\,} $$ |

tangent | opposite
/adjacent |
$$ {\displaystyle \tan \theta ={\frac {\sin \theta }{\cos \theta }}=\cot \left({\frac {\pi }{2}}-\theta \right)={\frac {1}{\cot \theta }}} $$ | $$ {\displaystyle \tan x={\frac {\sin x}{\cos x}}=\cot \left(90^{\circ }-x\right)={\frac {1}{\cot x}}} $$ |

cotangent | adjacent
/opposite |
$$ {\displaystyle \cot \theta ={\frac {\cos \theta }{\sin \theta }}=\tan \left({\frac {\pi }{2}}-\theta \right)={\frac {1}{\tan \theta }}} $$ | $$ {\displaystyle \cot x={\frac {\cos x}{\sin x}}=\tan \left(90^{\circ }-x\right)={\frac {1}{\tan x}}} $$ |

secant | hypotenuse
/adjacent |
$$ {\displaystyle \sec \theta =\csc \left({\frac {\pi }{2}}-\theta \right)={\frac {1}{\cos \theta }}} $$ | $$ {\displaystyle \sec x=\csc \left(90^{\circ }-x\right)={\frac {1}{\cos x}}} $$ |

cosecant | hypotenuse
/opposite |
$$ {\displaystyle \csc \theta =\sec \left({\frac {\pi }{2}}-\theta \right)={\frac {1}{\sin \theta }}} $$ | $$ {\displaystyle \csc x=\sec \left(90^{\circ }-x\right)={\frac {1}{\sin x}}} $$ |

Now we will resolve a couple of related examples to make your concept clear enough!

Find the value of each trigonometric ratio for the triangle given as under:

**Solution:**

Sine(Î¸) = Perpendicular/Hypotenuse

Sine(Î¸) = 0.8 (for angle calculations, tap sine calculator)

Cosine(Î¸) = Base/Hypotenuse

Cosine(Î¸) = 0.6 (for angle calculations, tap cosine calculator)

Tangent(Î¸) = Perpendicular/Base

Tangent(Î¸) = 1.33 (for angle calculations, tap tangent calculator)

Secant(Î¸) = Hypotenuse/Perpendicular

Secant(Î¸) = 1.25 (for angle calculations, tap Â secant calculator)

Cosecant(Î¸) = Hypotenuse/Base

Cosecant(Î¸) = 1.67 (for angle calculations, tap csc calculator)

Cotangent(Î¸) = Base/Perpendicular

Cotangent(Î¸) = 0.75 (for angle calculations, tap cotangent calculator)

Which are required trigonometric ratios for the given triangle and can also be double checked by an online find exact value of trig function calculator.

Compute the following trig ratios for different measures of triangle given as under:

Secant(Î¸) = ?

Cosine(Î¸) = ?

**Data given:**

Hypotenuse = 5.5

Perpendicular = 4

Base = 2.4

**Solution:**

Secant(Î¸) = Hypotenuse/Perpendicular

Secant(Î¸) = 5.5/4

Secant(Î¸) = 1.375

Cosine(Î¸) = Base/Hypotenuse

Cosine(Î¸) = 2.4 / 5.5

Cosine(Î¸) = 0.436

Now we will take you through the guide below that will help you to determine any trig function ratios by using this online six trigonometric functions calculator.

**Input:**

- In the first field, enter from the first drop-down list, select the trig function to me computed
- In the very next box, enter the measure of angle
- Now hit the calculate button

**Output:**

Our trig ratio calculator does the following calculations:

- Calculates the trig angle ratio in both degrees and radians
- Shows graphical interpretation of the angle function

Apart from angles only, you can also determine the sides of the right triangle by using another law of sines calculator.

Following are real life applications of trigonometry:

- Satellite systems
- Cartography
- Astrophysics
- Roof inclination projects
- Engineering
- Chemistry

In every distinctive field, the

Trigonometry is considered one of the best branches of mathematics. This is because it helps pupils or professionals to understand complex angle dimensions to design maps.

Trigonometry is basically the study of angle nature in any triangle. While on the other hand, calculus corresponds to the complicated and advanced query mathematics that lets you put in trouble with many complicated functions.

Greek mathematician Hipprachus introduced the concept of Trigonometry.

We are surrounded by numberless applications of trigonometry. And the angle ratio functions used in the subject are very crucial to understand map theory, design analytics, and complicated structure calculations. That is why we have developed this trigonometry calculator with steps so that you may solve for these functions without any hurdle.

From the source of Wikipedia: Trigonometry, ratios, Mnemonics, Trigonometric functions of real or complex variables, Inverse trigonometric functions, Applications

From the source of Khan Academy: Radians & degrees

From the source of Lumen Learning: Algebra and Trigonometry, Analytic Geometry