Sine, Cosine, and Tangent are the three basic functions of trigonometry through which trigonometric identities, trigonometry functions, and formulas are formed. The tangent is defined as the ratio of the length of the opposite side or perpendicular of a right angle to the angle and the length of the adjacent side. Tangent function in trigonometry is used to calculate the slope of a line between the origin and a point defining the intersection between hypotenuse and altitude of a right-angle triangle. In this article, we will discuss the tan 0 values and how to derive the tan 0 degrees value.

The Value of Tan 0 degrees equal to zero.

As we know, Sine, Cosine, and Tangent are the three basic functions of trigonometry. Let us brief about all the three basic functions with the help of a right-angle triangle.

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The Sine Function states that for a given right angle triangle, the Sin of angle θ is defined as the ratio of the length of the opposite side of a triangle to its hypotenuse.

Sin θ = Opposite side/ Hypotenuse.

The Cosine Function states that for a given right angle triangle, the Cosine of angle θ is defined as the ratio of the length of the adjacent side of a triangle to its hypotenuse.

Cos θ = Adjacent side / Hypotenuse.

The Tangent Function states that for a given right angle triangle, the Cosine of angle θ is defined as the ratio of the length of the opposite side of a triangle to the angle and the adjacent side.

Tan θ = Opposite side / Hypotenuse.

Also, the values of the sin of 0° and cos of 0° are used to find the value tan of 0°, but the condition is that sin 0°, and cos 0° must be from the same triangle. It is just a very basic concept of trigonometry to find the tangent of the angle using the sine and cosine of the angle. It is known that the ratio of sine and cosine of the same angle gives the tangent of the same angle. So, if we have the value of sin 0° degree and cos 0° degree, then the value of tan 0° degrees can be calculated very easily.

Accordingly, Tan θ = Sinθ/ Cosθ

Tan 0 degree in fraction can be expressed as,

Tan 0 degrees equal to Sin 0° / Cos 0°

We know than Sin 0 ° = 0 and Cos 0° = 1

Therefore, the Tan 0 is equal to 0/1 or 0.

It implies that Tan 0 is equal to 0.

Various tangent formulas can be formulated through a tangent function in trigonometry. The basic formula of the tangent which is mostly used is to solve questions is,

Tan θ = Perpendicular/ Base Or Tanθ = Sinθ/ Cosθ Or Tanθ = 1/Cotθ.

Tan (a+b) equals Tan (a) + Tan (b)/1- Tan (a) Tan (b)

Tan (90 +θ) = Cot θ

Tan (90 - θ) = - Cotθ

Tan (-θ) = Tanθ

Evaluate the following questions given below-

Question 1) Tan (90-45)°

Solution:

As we know, Tan (90-θ) = Cot θ

Tan (90 - 45) =Cot 45°

Cot 45° = 1

So accordingly,

Tan (90 - 45)° = 1

Hence, the value of Tan (90 - 45)° is 1.

Question 2) Find the value of Tan 150°

Solution:

Tan 150° = Tan (90 + 60)°

As we know,

Tan (90 + θ) = Cosθ

Tan (90 + 45) = Cos 45°

Cos 45° = 1

Accordingly,

Tan (90 + 45)° = 1.

FAQ (Frequently Asked Questions)

Question 1) Explain the Law of Tangents

Answer )The law of tangent represents the relationship between the tangent of two angles and the length of the opposite sides. The law of tangent is also applied in the triangles other than the right-angle triangle as it is equally important as the law of sine and law of cosines. The law of tan is used to find the remaining parts of a triangle if two angles and one side or two sides and one angle are given in the question which is also referred as SAS (side angle side) or ASA (angle-side-angle) from the perspective of congruence of triangle.

The three important information of an ordinary triangle is needed to understand the concept of the law of tangents. The value of the remaining parts of a triangle can be calculated through the concept of law of tangents if any of the information given below is given in the question.

Two sides and one opposite angle of any triangle

Anyone side and two angle

All three sides

Any two sides and the angle between them.

**Law of Tangents Formula**

(α - β)/(α + β) = tan {β - (α/2)}/tan (α+β)/2

Question 2) What is the Value of Tan 30°?

Answer) If an angle of a right-angled triangle is 30° degree, then the value of tan 30°, can be written as tan (30°) according to the Sexagesimal System. If fractional form tan 30°values 1/√3, which is equal to 0.5773502691. It is an irrational number.

Question 3) At What Angles Tangent is Equal to Zero?

Answer) As we all know, tangent is the ratio of sine and cosine; then, whenever the sin function has a value equal to zero, tan function tends to be zero. Hence, at the angles, 0°, 180°, 270° value of the tangent function is zero.