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Trigonometry  Calculator

Trigonometry Calculator

Select the trigonometric function and enter the angle in the designated field. The calculator will readily calculate its value with graph shown.

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This trigonometry calculator 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.

Working of This Right Triangle Trigonometry Calculator:

You can 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 compute.
  • 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.

What is Trigonometry and Trigonometric Ratios?

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

Sine:

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.

Cosine:

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

Tangent:

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

Formula:

Tangent = Perpendicular/Base

Secant:

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

Formula:

Secant = Hypotenuse/Perpendicular

Cosecant:

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

Cotangent:

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

Formula:

Cotangent = Base/Perpendicular

Formulas of Inverse Trigonometric Functions

Below are the formulas of all the inverse trigonometric functions:

Arcsine:

It is the inverse of sine function.

Formula:

Arcsin = sin^{-1}x

Arccos:

The inverse of the cosine function is termed as arccos.

Formula:

Arccos = cos^{-1}x

Arctan:

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

Formula:

Arctan = tan^{-1}x

Arccotangent:

The reciprocal of cotangent function is called arccotangent function.

Formula:

Arccot = cot^{-1}x

Arcsecant:

This particular function is actually the inverse of the secant function.

Formula:

Arcsec = sec^{-1}x

Arccosecant:

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 azimuthally. 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.

Summary of Trigonometric Functions:

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

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

Practical Example:

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

Solution:

Sine(θ) = Perpendicular/Hypotenuse

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

Cosine(θ) = Base/Hypotenuse

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

Tangent(θ) = Perpendicular/Base

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

Secant(θ) = Hypotenuse/Perpendicular

Secant(θ) = 1.25 (for angle calculations, tap  secant calculator)

Cosecant(θ) = Hypotenuse/Base

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

Cotangent(θ) = Base/Perpendicular

Cotangent(θ) = 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.

FAQs

How to Convert Decimal to Degrees in Trigonometry?

Here’s how you can convert decimal to degrees in trigonometry:

  • Find the relationship of trigonometry using SOHCAHTOA.
  • You can get the result by taking the inverse identity of the decimal.

How to Find the Height of a Triangle Using Trigonometry?

It is very easy to find the height of a triangle using trigonometry, have a look below.

  • First of all, draw a triangle and split it into two smaller triangles then mark the height.
  • You can solve the remaining triangles using trigonometry and find the height of the triangle.
  • After finding height, you can compare your answer with the answer of an online trigonometry calculator.

How Trigonometry is Used in Real Life?

Following are real life applications of trigonometry:

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

Is Trigonometry Harder Than Calculus?

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.

References:

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