Tan 30 Degrees In Fraction

Tan sixty Value: Formula, Solved Examples

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Tan 60: Tan 60 value is 1.73205080757 or √iii. Tan is ane of the most important trigonometric functions other than Sin and Cos and remembering the values for these functions is really of import as near all the questions asked in the examination from the topic involve using these values. The tan role of an angle is equal to the length of the opposite side divided by the length of the adjacent side. In this article, nosotros will provide yous with all the details on Tan 60 and other values of Tanθ at θ = 0, thirty, 45…180, 270, 360.

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

Tan 60 Degrees Value

Earlier finding out the value of Tan lx 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 = \(\frac{Perpendicular}{Base of operations}\) = a/b

Why is Tan 60 Root 3?

To answer the in a higher place query nosotros will have an equilateral triangle with each angle equal to 60 degrees.

Here, ∠A = ∠B = ∠C = 60°
Now we depict a perpendicular Advertizement from A to BC. Taking triangle, ABD and ADC, Nosotros go, ∠ ADB = ∠ADC= 90° and ∠ ABD = ∠ACD= 60°. Hence, AD=AD.
Using AAS Congruency, nosotros take Δ ABD ≅ Δ ACD and then, BD = DC
Now taking, AB = BC =2a, and then BD= ½ (BC) =½ (2a) =a.
By Pythagoras theorem, ABⁱⁱ= Advert²– BDⁱⁱ, Advert²= ABⁱⁱ-BD², Advertizement² =(2a)^two – aⁱⁱ, Ad²= 4a²-a², AD² = 3aⁱⁱ. Hence, Advertisement=a√three.
For triangle ADB, Tan 60⁰= Advertizement/BD = a√iii/a = √3
Therefore, tan 60 degrees equals √three.

Tangent, Cosine, Sine Functions

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

Degrees	0°	30°	45°	60°	90°	180°	270°	360°
Sin	0	1/two	1/√ii	√3/two	i	0	-one	0
Cos	ane	√3/2	1/√2	1/2	0	-one	0	ane
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 lot can use them to find other functions like Cosec, Sec, and Cot.

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

Angles	0°	xxx°or π/6	45°or π/iv	60°or π/3	90° or π/2	180°or π	270°or 3π/2	360°or 2π
Sin	0	1/two	1/√2	√3/2	1	0	−i	0
Cos	1	√3/ii	1/√2	one/2	0	−i	0	1
Tan	0	i/√three	1	√3	Not Divers	0	Not Defined	0
Cot	Not Defined	√3	1	1/√3	0	Non Defined	0	Not Defined
Cosec	Non Defined	two	√2	2/√3	ane	Non Defined	−ane	Not Divers
Sec	1	2/√iii	√2	2	Not Defined	−ane	Non Defined	1

Compound Angles Formulae

Here are some important formulae that volition aid you in solving questions.

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

Learn on Embibe

Students can access the following free written report materials on Embibe for their examination preparation:

NCERT Solutions	NCERT Books
Class 8 Mock Test Series	Class viii Practice Questions
Class 9 Mock Test Series	Class 9 Exercise Questions
Course 10 Mock Exam Serial	Form x Practice Questions
JEE Main Mock Tests (Form xi-12 PCM)	JEE Primary Do Questions (Class xi-12 PCM)
NEET Mock Tests (Course 11-12 PCB)	NEET Exercise Questions (Grade 11-12 PCB)

FAQs on Tan sixty Value

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

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

Q2. What is tan sixty as a fraction?
Ans. The value of Tan threescore° equally a fraction is √iii.

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 xc is equal to 1.

So that was all on Tan lx and nosotros hope the information provided to you on this page was helpful. However, if you have further questions experience gratuitous to employ the comments section.

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