# Tan 30 degrees

## Tan 30 degrees

The value of tan30 is 1/√3. If we solved 1√3 we got 0.57735026919. tan 30 degrees is also represented by tan π/6 in terms of radians.

tan30 = 1/√3 = 0.57735026919

### How to calculate the value of tan30∘

There are so many ways of calculating the values of tan30 .

### First Method :- Calculate the value of tan30∘

by using sin∅ & cos∅

We know that tan∅ = Sin∅/Cos∅

Sin∅ = Perpendicular/Hypotenuse Suppose for a triangle for PQR right angle at Q. ∅ is the angle  , PR is the hypotenuse . QR is the base and  PQ is the Opposite side or perpendicular.

So we can say that

Sin∅ = Perpendicular/Hypotenuse = PQ/PR

Similarly

Cos∅ = Base /Hypotenuse = QR/PR  (∵ ∆ PQR )

Now can say that tan∅ = Sin∅/Cos∅ Now  tan∅ = PQ/QR

tan∅ = Perpendicular/Base

### If we know the value of sin30∘ and cos30∘. We can easily find the value of tan30∘.

We know that  sin30= 1/2 and  Cos30= √3/2

So we know tan∅ = Sin∅/Cos∅

= tan∅ = sin30/Cos30

= = tan∅ = 1/√3  { ∵ tan30= 1/ √3  }

### If we know the value of sin30∘ . We can easily find the value of tan30∘.

We know that  sin30= 1/2    { ∵ Sin∅ = Perpendicular/Hypotenuse = 1/2 } Now we are find base ( QR ) by using the Pythagoras Theorem

= ( Perpendicular )2 + (Base)2 = (Hypotenuse )2

= ( 1 )2 + ( QR )2 = (2)2

= 1  + ( QR )2 = 4

= ( QR )2 =4-1

= ( QR ) = √3

So tan∅ = Perpendicular/Base  {  ∵ tan∅ = PQ/QR }

= tan30= 1/ √3

### If we know the value of Cos30∘ . We can easily find the value of tan30∘.

We know that  Cos30= √3/2     { ∵ Cos∅ = Base /Hypotenuse = √3/2   } Now we are find Perpendicular ( PQ ) by using the Pythagoras Theorem

= ( Perpendicular )2 + (Base)2 = (Hypotenuse )2

= ( PQ )2 + ( √3 )2 = (2)2

=  ( PQ )2  + 3 = 4

= ( PQ)2 =4-3

= ( PQ ) = √1

So tan∅ = Perpendicular/Base  {  ∵ tan∅ = PQ/QR }

= tan30= 1/ √3

### If we know the value of Sec30∘. We can easily find the value of tan30∘.

We know that  Sec30 = 2/√3     { ∵ Sec∅ = Hypotenuse/Base = 2/√3 } Now we are find Perpendicular ( PQ ) by using the Pythagoras Theorem

= ( Perpendicular )2 + (Base)2 = (Hypotenuse )2

= ( PQ )2 + ( √3 )2 = (2)2

=  ( PQ )2  + 3 = 4

= ( PQ)2 =4-3

= ( PQ ) = √1

So tan∅ = Perpendicular/Base   {  ∵ tan∅ = PQ/QR }

= tan30= 1/ √3

### If we know the value of  Cosec30 . We can easily find the value of tan30∘.

We know that  Cosec30 = 2    { ∵ Cosec∅ = Hypotenuse/Perpendicular = 2/1 } Now we are find Base ( QR ) by using the Pythagoras Theorem

= ( Perpendicular )2 + (Base)2 = (Hypotenuse )2

= ( 1 )2 + (QR)2 = (2 )2

= ( QR )2 + ( 1)2 = (2)2

=  ( QR )2  + 1 = 4

= ( QR)2 =4-1

= ( QR ) = √3

So tan∅ = Perpendicular/Base   {  ∵ tan∅ = PQ/QR }

= tan30= 1/ √3

Check the trigonometry table to get the values for all trigonometry ratios.

### Trigonometry Formulas Tan 30 degrees

• tan∅ = 1/cot∅ , cot∅ = 1/tan∅
• tan∅.cot∅ = 1
• tan∅ = sin∅/cos∅
• tan(A+B) = tanA + tanB /1-tanA tanB
• tan(A-B) = tanA-tanB/1+tanAtanB
• tan2A = 2tanA/1- tan2

= 1- tan2A/1 +tan2A

• tan3A = 3tanA-tan3A /1-3tan3A
• tanA = 2tan(A/2) / 1-tan2(A/2)
• tan(A+B+C) = tanA+tanB+tanC-tanAtanBtanC / 1-tanAtanB-tanBtanC -tanAtanC
• tanA tan2A tan4A = tan3A  