Sin3A Cos3A Tan3A Formulas

On this page sin3A cos3A tan3A formulas we are going to see the formulas in trigonometry.These are the formulas that we are using in trigonometry to simplify.

Here you can find example problems to show the purpose of these formulas.

  • Sin 3A = 3 Sin A - 4 sin³A
  • Cos 3A = 4 Cos³A - 3 Cos A
  • tan 3A = (3 tan A - tan³ A)/(1-3tan²A)

Now we are going to see example problems based on the above formulas.

Example problems using sin3A cos3A tan3A formulas

Example 1:

If sin A  = 3/5 then find the value of sin 3A.

Solution :

In this problem we have given the value of Sin A. Now we need to find the value of sin 3A.

To solve this problem we have a formula for sin 3A.In this formula we have to plug 3/5 instead of the term sin A.

            Sin 3A = 3 Sin A - 4 sin³A

sin 3A = 3 (3/5) - 4 (3/5)³

sin 3A = 9/5 - 4 (9/25)

  =  9/5 - 36/25

  =  (9/5) x (5/5)  - 3/25

  =  45/25 - 3/25

  =  (45-3)/25

  =  42/25

Example 2 :

Prove that  8 cos³ Π/9 - 6 cos Π/9 = 1

Solution :

 8 cos³ Π/9 - 6 cos Π/9 = 1

To solve this problem, first we have factor out from both terms.We can split 8 as 2 times 4 and 6 as 2 times 3. After factor out 3 it looks like a formula.

2[4cos³ Π/9 - 3 cos Π/9]

         Cos 3A = 4 Cos³A - 3 Cos A

  =  2[4cos³ Π/9 - 3 cos Π/9]

  =  2cos 3(Π/9)

  =  2cos (3Π/9)

  =  2cos Π/3

  =  2 x v3/2  ==>  v3  

Example 3 :

 If tan A = 3 find the value of tan 3A

Solution :

tan 3A = (3 tan A - tan³ A)/(1-3tan²A)

  =  [3 (3) - (3)³] /[1-3(3)²]

  =  [9 - 27]/[1-27]

  =  (-18)/(-26)

  =  9/13

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