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Cofunction Calculator

Cofunction Calculator

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Angle(x):

 

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Use a Cofunction calculator to find a complement  of trigonometric identities (sin, cos, tan, sec, cosec, cot).The Cofunction identity calculator simply explains the relationship between the ratios. 

The trigonometric ratios have reciprocal identities and Mathematicians define them as reciprocal identities

Definition of Cofunction?

“A Cofunction is a function whose value for the complement of an angle is equal to the value of a trigonometric function of the angle itself”
In a Cofunction the trigonometric function where the complement values are equal to the complement trigonometric ratio.

Cofunction Identities in Radians, and Degrees are given below:

Cofunction(Radian) Cofunction(Degree)
sin (π/2 – θ) = cos θ sin (90° – θ) = cos θ
cos (π/2 – θ) = sin θ cos (90° – θ) = sin θ
tan (π/2 – θ) = cot θ tan (90° – θ) = cot θ
cot (π/2 – θ) = tan θ cot (90° – θ) = tan θ
sec (π/2 – θ) = cosec θ sec (90° – θ) = cosec θ
csc (π/2 – θ) = sec θ csc (90° – θ) = sec θ

Cofunction calculator online determines Cofunction Identities in Radians and Degrees

How to find a cofunction(trigonometric identities)?

The conjunction identities represent the relationship between the trigonometric identities, the value of the conjunction can only be measured if we are able to find the complement angle.The Cofunction always has the same values for a particular angle:

For example:

Sin(30)=Cos(60) = 0.76604444311898

The Cofunction equations calculator also helps to find the complement of an angle against which values of a trigonometric ratio are the same. The cofunction of a complementary angle calculator readily indicates the corresponding complementary angle.

Remember! The Sum of the complement angles is equal to 90°

What is a Cofunction?

Before understanding the basic concept of the Cofunction, it is essential to know what are the complement angles. This complement trigonometric ratio is also known as the reciprocal trigonometric ratio. We can find the complement angle of any trigonometric ratio by the  cotangent-calculator. Finding the cofunction can be a little confusing, but you can use the cofunction equations calculator to find cofunction easily.For example, when we enter the values of the “Sin” and “Cos” in calculator we find the cofunction of “Sin” and “Cos”.For this we have to study the Law of Sines and Law of Cosines. For measuring the angle values, we can use the Law of Sines Calculator, and Law of Cosines calculator.

The Cofunction of Sin:

The conjunction of the Sin is Cos and vice versa, but there is no direct interconvertible. Against all the values of the Sin θ, we can find the complement values by subtracting the 90 ° from the angle(θ – 90).We can use a cofunction to write an expression equal to calculator value.

θ Sin( θ ) θ – 90 Cos ( θ )
50 ° sin(50 ) = 0.76604444311898 90 – 50 = 40 ° cos(40 ) = 0.76604444311898
60 ° sin(60 ) = 0.86602540378444 90 – 60 = 30 ° cos(30 ) = 0.86602540378444
70 ° sin(70 ) = 0.93969262078591 90 – 70 = 20 ° cos(20 ) = 0.93969262078591
80 ° sin(80 ) = 0.98480775301221 90 – 80 = 10 ° cos(10 ) = 0.98480775301221

By using a handy cofunction calculator can find the equivalent values of the angle in a matter of seconds.

What is the Cofunction of Tan?

We already know that the Co Function equations for sine and cosine are:

sin(θ) / cos(θ) = cos(90o – θ)/sin(90o – θ). 

We know that:

cos/sin=cot 

Substituting Cofunction values, We get: 

 cos(90o – θ) / sin(90o – θ) = cot(90o – θ). 

Thus, 

tan(θ) = cot(90o – θ) 

The table below has Cofunctions of the “tan θ”, we can use the cofunction identities calculator for the “tan θ” cofunctions: 

θ tan( θ ) θ – 90 Cot ( θ )
50 ° tan(50 ) = 1.19175359259 90 – 50 = 40 ° cot(40 ) = 1.19175359259
60 ° tan (60) = 1.73205080757 90 – 60 = 30 ° cot(30 ) = 1.73205080757
70 ° tan(70 ) = 2.74747741945 90 – 70 = 20 ° cot(20 ) = 2.74747741945
80 ° tan(80 ) = 5.67128181962 90 – 80 = 10 ° cot(10 ) = 5.67128181962

Cofunction theorem calculator finds the Cofunction of “tan” by using the Cofunction theorem

Working of the Cofunction Calculator:

The following input values for the cofunction identities calculator are required:

Input:

  • Select the trigonometric ratio
  • Enter the angle
  • Choose the radian/degree
  • Hit the calculate button to find Cofunction

Output:

The Cofunction identities calculator displays the following output value:

  • Complementary angles along with Cofunction are measured

FAQS:

Why do we relate Cofunction with trigonometric ratios?

The Confusion simply relates to the relationship between the Sin, Cos, Tan, Cot, Sec, and Cosec. The cofunction identities calculator is superb to find the complement angles.

What is the Cofunction Theorem?

The Cofunction Theorem describes that any trigonometric function of the acute angle is equal to its Cofunction of the complementary angle. The cofunction calculator measures all the values according to the conduction theorem.

What is the value of the complementary angle in Radian?

The value of the complementary angles in Radians is π/2. find a cofunction with the same value as the given expression in degrees and convert it into the radian by the Co function equations calculator.

What is meant by the complement cofunction?

The complement conjunction has the same values at different angles like 

tan(70 ) =cot(20 )= 2.74747741945. Find the cofunction calculator to make the calculation easy for yourself.

What is the Cofunction of tan (90 – x)?

We can normally express the Cofunction of the tan(90-x)=cot x or cot (90 – x) = tan x, the cofunction calculator online makes it possible to find the cofunction easily.

What is the cofunction of CSC?

The CSC is actually the abbreviation of the trigonometric function Cosecant.The trigonometric identity Secant is the cofunction of the  Cosecant

Conclusion:

The cofunction measures the trigonometric ratio or circular function in radians or degrees in a precise manner. The cofunction actually represents the corresponding equal value of the trigonometric ratio in another ratio. The free online cofunction calculator finds values of trigonometric ratios in degree or in radian in a matter of seconds.

References:

From the source of Wikipedia: Cofunction, Cofunction identities

From the source of Study.com:Using Cofunction Identities,Trigonometry