Tan 60 Value: Formula, Solved Examples

Tan 60: Tan 60 value is 1.73205080757 or √3. Tan is one of the most important trigonometric functions other than Sin and Cos and remembering the values for these functions is really important as almost all the questions asked in the exam from the topic involve using these values. The tan function of an angle is equal to the length of the opposite side divided by the length of the adjacent side. In this article, we will provide you with all the details on Tan 60 and other values of Tanθ at θ = 0, 30, 45…180, 270, 360.

In a right-angled triangle, the side opposite of the right angle is called the hypotenuse side, the side opposite the angle of interest is called the opposite side and the remaining side is called the adjacent side where it forms a side of both the angle of interest and the right angle. So let us begin!

Tan 60 Degrees Value

Before finding out the value of Tan 60 degrees let us see what tan represents or is equivalent to. Since we know that Sin = Perpendicular/Hypotenuse, Cos = Base/Hypotenuse and we know that Tan = Sin/Cos = (Perpendicular/Hypotenuse) ÷ (Base/Hypotenuse) = Perpendicular/Base.

So, Tan = \(\frac{Perpendicular}{Base}\) = a/b

Why is Tan 60 Root 3?

To answer the above query we will take an equilateral triangle with each angle equal to 60 degrees.

Here, ∠A = ∠B = ∠C = 60°
Now we draw a perpendicular AD from A to BC. Taking triangle, ABD and ADC, We get, ∠ ADB = ∠ADC= 90° and ∠ ABD = ∠ACD= 60°. Hence, AD=AD.
Using AAS Congruency, we have Δ ABD ≅ Δ ACD so, BD = DC
Now taking, AB = BC =2a, so BD= ½ (BC) =½ (2a) =a.
By Pythagoras theorem, AB²= AD²– BD², AD²= AB²-BD², AD² =(2a)² – a², AD²= 4a²-a², AD² = 3a². Hence, AD=a√3.
For triangle ADB, Tan 60⁰= AD/BD = a√3/a = √3
Therefore, tan 60 degrees equals √3.

Tangent, Cosine, Sine Functions

Using the below derivation we can derive other trigonometric functions as well:

Degrees	0°	30°	45°	60°	90°	180°	270°	360°
Sin	0	1/2	1/√2	√3/2	1	0	-1	0
Cos	1	√3/2	1/√2	1/2	0	-1	0	1
Tan	0	1/√3	1	√3	∞	0	∞	0

Trigonometric Functions Table

Now that you know how to service the trigonometric functions and the values for them. You can use them to find other functions like Cosec, Sec, and Cot.

Cosec = 1/Sin
Sec = 1/Cos
Cot = 1/Tan or Cos/Sin

Angles	0°	30° or π/6	45° or π/4	60° or π/3	90° or π/2	180° or π	270° or 3π/2	360° or 2π
Sin	0	1/2	1/√2	√3/2	1	0	−1	0
Cos	1	√3/2	1/√2	1/2	0	−1	0	1
Tan	0	1/√3	1	√3	Not Defined	0	Not Defined	0
Cot	Not Defined	√3	1	1/√3	0	Not Defined	0	Not Defined
Cosec	Not Defined	2	√2	2/√3	1	Not Defined	−1	Not Defined
Sec	1	2/√3	√2	2	Not Defined	−1	Not Defined	1

Compound Angles Formulae

Here are some important formulae that will help you in solving questions.

(i) Tan (A + B) = (Tan A + Tan B) ÷ (1 − Tan A tan B)
(ii) Tan (A – B) = (Tan A − Tan B) ÷ (1 + Tan A Tan B)
(iii) Tan 2A = (2 Tan A) ÷ (1 – Tan² A)
(iv) Tan 3A = (3 Tan A – Tan³ A) ÷ (1 – 3Tan² A)

Learn on Embibe

Students can access the following study materials on Embibe for their exam preparation:

NCERT Solutions	NCERT Books
Class 8 Mock Test Series	Class 8 Practice Questions
Class 9 Mock Test Series	Class 9 Practice Questions
Class 10 Mock Test Series	Class 10 Practice Questions
JEE Main Mock Tests (Class 11-12 PCM)	JEE Main Practice Questions (Class 11-12 PCM)
NEET Mock Tests (Class 11-12 PCB)	NEET Practice Questions (Class 11-12 PCB)

FAQs on Tan 60 Value

Check out some questions that are commonly searched on the topic:

Q1. What is the exact value of Tan 60?
Ans. 1.73205080757 or √3 is the exact value of Tan 60.

Q2. What is tan 60 as a fraction?
Ans. The value of Tan 60° as a fraction is √3.

Q3. Is tan 60 degrees greater or less than 1?
Ans. Tan 60 is greater than 1 because its exact value is 1.732050…

Q4. What is the formula for tan θ?
Ans. The tan θ is equal to sin θ divided by cos θ.

Q5. What is the formula for tan 90?
Ans. Tan 90 is equal to 1.

So that was all on Tan 60 and we hope the information provided to you on this page was helpful. However, if you have further questions feel to use the comments section.

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