Sin3A Cos3A  Tan3A Formulas



In 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 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 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 to take 2 commonly from both terms.We can split 8 as 2 times 4 and 6 as 2 times 3.After taking 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
These are the example problems of sin3A cos3A tan3A formulas.

Related Topics

  1. Trigonometric Ratios
  2. Trigonometric Identities
  3. Complementary Angles In Trigonometry
  4. Values Of Certain Angles
  5. Heights And Distances
  6. Double Angle Formulas
  7. Half Angle Formulas
  8. Compound Angle Formulas
  9. 3A formulas
  10. Compound angles sum and differences
  11. Sum to product forms
  12. Trigonometry Problems Using Identities
  13. Trigonometry Practical Problems

Quote on Mathematics

“Mathematics, without this we can do nothing in our life. Each and everything around us is math.

Math is not only solving problems and finding solutions and it is also doing many things in our day to day life.  They are: 

It subtracts sadness and adds happiness in our life.    

It divides sorrow and multiplies forgiveness and love.

Some people would not be able accept that the subject Math is easy to understand. That is because; they are unable to realize how the life is complicated. The problems in the subject Math are easier to solve than the problems in our real life. When we people are able to solve all the problems in the complicated life, why can we not solve the simple math problems?

Many people think that the subject math is always complicated and it exists to make things from simple to complicate. But the real existence of the subject math is to make things from complicate to simple.”



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