COMPOUND ANGLES





In this page compound angles we are going to see all the formulas in trigonometry.Also we are going to see the example problems.

1. Sin (A+B) = Sin A Cos B + Cos A Sin B

2. Sin (A+B) = Sin A Cos B + Cos A Sin B


3. Cos (A+B) = Cos A Cos B - Sin A Sin B

4. Cos (A-B) = Cos A Cos B + Sin A Sin B


5.Tan (A+B) = [Tan A + Tan B] /(1- Tan A Tan B)

6.Tan (A-B) = [Tan A - Tan B] /(1+ Tan A Tan B)


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

Example 1:

Find the value of Cos 15°

Solution:

We don't have direct values for Cos 15° so we have to write 15° in mixed form of two angles.

Cos 15° = Cos (45°-30°)

This looks like in the form of Cos (A-B). So we have to apply the formula

Cos (A-B) = Cos A Cos B + Sin A Sin B

Cos (45°-30°) = Cos 45° Cos 30° + sin 45° Sin 30°

                    = (1/√2) x (√3/2) + (1/√2) x (1/2)

                    = (√3/2√2) + (1/2√2) 

                    = (√3 + 1)/2√2


Example 2:

Find the value of Cos 105°

Solution:

We don't have direct values for Cos 15° so we have to write 15° in mixed form of two angles.

Cos 105° = Cos (60°+45°)

This looks like in the form of Cos (A+B). So we have to apply the formula

Cos (A+B) = Cos A Cos B - Sin A Sin B

Cos (60°+45°) = Cos 60° Cos 45° + sin 60° Sin 45°

                    = (1/2) x (1/√2) + (√3/2) x (1/√2)

                    = (1/2√2) + (√3/2√2) 

                    = (1 + √3)/2√2        

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. 3A formulas
  9. Compound angles sum and differences
  10. Sum to product forms
  11. Trigonometry Problems Using Identities
  12. 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.”









Compound Angles to Trigonometry
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