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. The 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.
What is the Value of Tan 0 Degrees Equal to?
The Value of Tan 0 degrees is equal to zero.
Derivation of the Tan 0 Degree
As we know, Sine, Cosine, and Tangent are the three basic functions of trigonometry. Let us brief all the three basic functions with the help of a right-angle triangle.
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What is Sine Function?
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.
What is Cosine Function?
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.
What is Tangent Function?
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.
Find Tan 0° Using Sin and Cos
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.
Trigonometry Equations on the Basis of Tangent Function
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.
Other Tangent Formulas are:
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
Trigonometry Ratio Table of Different Angles
Angle | 0° | 30° | 45° | 60° | 90° | 180° | 270° | 360° |
sin | \[\frac{1}{2}\] | \[\frac{1}{\sqrt{2}}\] | \[\frac{\sqrt{3}}{2}\] | 1 | -1 | |||
cos | 1 | \[\frac{\sqrt{3}}{2}\] | \[\frac{1}{\sqrt{2}}\] | \[\frac{1}{2}\] | -1 | 1 | ||
tan | \[\frac{1}{\sqrt{3}}\] | 1 | \[\sqrt{3}\] | ∞ | ∞ | 1 | ||
cot | ∞ | \[\sqrt{3}\] | 1 | \[\frac{1}{\sqrt{2}}\] | ∞ | ∞ | ||
csc | ∞ | 2 | \[\sqrt{2}\] | \[\frac{2}{\sqrt{3}}\] | 1 | ∞ | -1 | ∞ |
sec | 1 | \[\frac{2}{\sqrt{3}}\] | \[\sqrt{2}\] | 2 | ∞ | -1 | ∞ | 1 |
Questions to be Solved
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.
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Tan 0 Value
The three basic functions of trigonometry are Sine, Cosine, and Tangent, through which the trigonometric identities, the trigonometric functions, and formulas are formed. The tangent can be 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 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.
Hypotenuse side: In a right-angled triangle, it is the opposite side of the right angle. Hypotenuse is the longest side of any right-angled triangle, opposite the right angle. The side that is opposite the angle of interest is called the opposite side and the remaining side is known as the adjacent side, where it forms a side of both the right angle and the angle of interest.
Derivation of the Tan 0 Degree.
The sine function and cosine function is used in order to find the value of tan 0 degrees as the tan function is the ratio of the sine function and cos function.
The values of tangent degrees can be found with the help of the sine functions and cosine functions. By knowing the value of sine functions, we will be able to find the values of cos and tan functions.
The values of the sin of 0° and cos of 0° are used to find the value tan of 0°, provided sin 0°, and cos 0° is from the same triangle.
Tangent formulas can be formulated through a tangent function .The basic formula of the tangent which is mostly used is to solve questions is,
Tan θ = Perpendicular/ Base Or Tanθ = Sinθ/ Cosθ Or Tan Θ = 1/Cosθ.
Other Tangent Formulas are:
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.
The Law of Tangents formula : (α - β)/(α + β) = tan {β - (α/2)}/tan (α+β)/2
