Cofunções calculator - sin, cos, tan, cot, sec, csc | steps (2023)

Becofunction calculatorIt's about trigonometry. Six functions describe the relationships between sides and angles. Since they are related, we have grouped them in pairs: sin and cos, tan and cot, sec and csc. That's why our calculator tells you what they are and how to calculate them.

You will also learn abouttrigonometric functionsand its use in geometry. For more geometry andTrigonometryrelated posts and questions and other math articles, search our database of various calculators and find your answer.

What is co-function? Definition of cofunction

ACow functionis a trigonometric function where the value of its complement is equal to the value of the given trigonometric function of angle. The definition of a co-function in mathematics relates to trigonometric functions. We can say that for exampleBreasteCosineconfuse each other. Also, you can learn more about these features with ourLaw of cosineselaw of sineCalculator.

The same theory applies to bothdesiccantcut offeThe keytouch. Writing a function helps solve a trigonometric equation in terms of its cofunction. For example, the simplest example is the equation where\sin A = \cosB.

In fact, a cofunction is a type of function that performs two different tasks. For example, a co-function can calculate the area of ​​a rectangle and the perimeter of a rectangle.

trigonometric functions

In the ancient Greeks, the word "trigonometry" meant "three" and the word "gon" meant angles. If you are interested in the side length of atriangle, its angles and its surface, knowledge of trigonometry will undoubtedly help you and answer all your questions.

Trigonometric functions have six essential parts: sine, cosine, secant, cosecant, tangent, and cotangent. Its domain input value is the angle of a right triangle and the numeric response is an interval. Also the trigonometric functionf(x)=\sin\thetahas a domain whose angle θ is specified in radians or degrees and an interval of [-1, 1]. We also have a number and part of other features. Likewise, we have a domain and reach of all other functions.

Trigonometric functions and their identities are the ratios of the sides of a right triangle. Use the sides of a right triangle to calculate sine, cosine, tangent, secant, cosecant, and cotangent values. The sides of a right triangle are the perpendicular side, the hypotenuse, and the base.

The cofunction graphs: sin and cos, tan and cot, sec and csc

Sine and cosine (sin and cos), tangent and cotangent (tan and cot), and secant and cosecane (sec and csc) are six trigonometric functions.

Thus, each pair has a "basic" function and a function of the same name that it precedes"co."For each we say that one is a co-function of the other. In addition, below we will compare the diagrams of the functions on the right and explain their similarities.

sin and cos

First of all, sine and cosine are trigonometric functions that we usecalculationthe angles of the triangle. You can use it to find the side length of a triangle in geometry. The unit of measurement is radians. The sine is the ratio of the length of the opposite side to the length of the hypotenuse.

The paths are equal in the range 0 to 90 degrees - sine 0 to 90 and cosine 90 to 0.

Cofunções calculator - sin, cos, tan, cot, sec, csc | steps (1)

Tan and Crib

Second, we can explain the tanning and cot graphs. We can say that the tangent is a ratio of the opposite side to the adjacent side of a righttriangle.

On the other hand, the cotangent is a ratio between the adjacent and opposite sides of a right triangle. If you follow the tangent curve from 0 to 90 and the cotangent curve from 90 to 0, you will see that they follow a similar path.

Cofunções calculator - sin, cos, tan, cot, sec, csc | steps (2)

Seg and Csc

Third, we have the example of the sec and csc functions. Secant and kosekan are the reciprocal functions of cosine and sine. Secant is the ratio of the length of the hypotenuse to the adjacent side of atriangle.

On the other hand, the cosecane is the ratio between the size of the hypotenuse and the length of the opposite side of a right triangle.

Cofunções calculator - sin, cos, tan, cot, sec, csc | steps (3)

Co-function identities in the Degrees table

The system consists of threeidentities, each containing two trigonometric functions.

  • The first identity, sin(x)cos(y), can be found by drawing a line from the origin to the point (x,y) and then finding the point on the line that has the same x-coordinate as the point (x,y). So this point is the point (x',y'), and the identity can be found by taking the sine of x' and the cosine of y'.
  • The second identity, cos(x)sin(y), can be found by drawing a line from the origin to the point (x,y) and then finding the point on the line that has the same y-coordinate as the point ( x,y ). So this point is the point (x',y'), and the identity can be found by taking the cosine of x' and the sine of y'.
  • The third identity, tan(x)cot(y), can be found by drawing a line from the origin to the point (x,y) and then finding the point on the line that has the same y-coordinate as the point ( x,y ).
\sin (90 - x) = \cos x \leftrightarrow \cos (90 - x) = \sin x
\tan (90 - x) = \cot x \leftrightarrow \cot (90 - x) = \tan x
\sec (90 - x) = \csc x \leftrightarrow \csc (90 - x) = \sec x

Co-function identities in the radians table

With a focus on math and science, this table provides a concise and straightforward way to identify co-function identities in radians. It also shows how to find the cosine and sine of a given angle in radians.

Cofunções calculator - sin, cos, tan, cot, sec, csc | steps (4)

Finding the Cofunction: Cofunction Identities

You've probably heard the term "co-function" before, but you know what it means and how you can benefit from it. This function is a "reciprocal" function or inverse function in our calculator. To find a function, you need to know the reciprocal of the function.

As an example, let's assume that the configuration of the function "x + 1" is equal to "1/x". Follow the steps below to find the role you're looking for. First you need to find the equation of the function and write it in its standard form. Second, if the equation is "x + 1 = 1", you need to simplify the equation by dividing by "x + 1". In the end we get "1 = 1", which gives us the answer that the function "x + 1" is equal to "1/x".

In addition, identity configurations are derived to obtain identity sums and differences for sine and tangent functions. The identities of the structures are derived directly from the identity of the difference with the cosine. Meager,co-functional identitiesrepresent the relationship between the trigonometric functions. Make sure you see thisCalculator for sum and difference identities.

Identities of trigonometric cofunctions are a set of formulas relating the trigonometric functions of complementary angles. Complementary angles are two angles whose sum equals 90 degrees or π/2 radians. For example, 30 degrees and 60 degrees are complementary angles, as are π/6 radians and π/3 radians.

The six trigonometric functions are sine, cosine, tangent, cotangent, secant, and cosecant. Each of these functions has a co-function defined as a function of the complementary angle. For example, the sine co-function is cosine, the cosine co-function is sine, and so on.

The identities of the trigonometric cofunctions are as follows:

sin(θ) = cos(π/2 – θ)

cos(θ) = sin(π/2 – θ)

tan(θ) = Kinderbett(π/2 – θ)

Kinderbett(θ) = tan(π/2 – θ)

Segment(θ) = csc(π/2 – θ)

csc(θ) = seg(π/2 – θ)

These identities can be derived using the definitions of trigonometric functions and the fact that the sum of the complementary angles is 90 degrees. For example, to derive the first identity, we start with the definition of sine:

sin(θ) = inverse/hypotenuse

Next we draw a right triangle with angle θ and its complementary angle (π/2 – θ). The opposite side of θ becomes the adjacent side of (π/2 - θ), and the hypotenuse is the same for both angles. With the definition of the cosine we can write:

cos(π/2 – θ) = required/Hypotenuse

Substituting the found values ​​for Opposites and Adjacent, we get:

cos(π/2 – θ) = inverse/hypotenuse = sin(θ)

Similarly, we can derive the other five co-function identities using the same method and substituting the corresponding trigonometric functions.

Trigonometric identities of cofunctions are useful for simplifying trigonometric expressions and solving trigonometric equations. For example, if we have an expression involving sine and cosine, we can use the identity sin(θ) = cos(π/2 – θ) to rewrite it entirely as sine or cosine.

Example: Using the Cofunction Calculator

Using a practical example, we show how ourscalculatorIt works out. Let's say you have decided to decorate your room. More precisely, the floor is to be repaired in order to replace the tiles with parquet. However, if your room doesn't have perfect measurements, then it's not a regular rectangle. You need a cosine of 55 degrees and a cotangent of 40 degrees to get results.

We assume you don't remember the trigonometry formula for cosines and cotangents. For these reasons, this calculator is a great solution to get the desired result as quickly as possible with a simple number entry.

Everything looks so much easier when you have a function calculator. Your first task is to choose the role you have. The example we gave is the cosine, whose notation is cos(x). Next you need to go to the box below and contain the corner. Enter the angle value u = 55° in this field and after this step our co-function calculator will provide you with a solution.

The same procedure applies to the second case. You just select the cotangent labeled (cot(x)) and enter 30°. In summary, this calculator is very easy and simple to use once you know the values.

Frequently Asked Questions

How do you find the cofunction?

ÖCow functiondemonstrates the relationship between sine - cosine, tangent - cotangent and secant - cosecane. The value of a trigonometric function of an angle has the same result as the value of the cofunction of its complement.

What is the cofunction of tan?

We can express the cofunction of tan as tan(90 - x) = cot x or cot(90 - x) = tan x.

How do you find the co-role of a CSC?

You can find the cofunction of a csc as sec(90 - x) = csc x.

How do you prove co-function identities?

You can find the proof of co-function identities by constructing an equivalent equation with an equivalent set of variables. For example, for all possible values ​​of x and y, the following equation holds: x = y + 1. By substituting the variable x for the variable y, the identity of the cofunction was converted into an equivalent equation.

What is the cofunction theorem?

This theorem states that every acute angle trigonometric function is equal to its complementary angle cofunction.


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