**Summary**

Compound angle formulas are:

Half angle formulas are:

Function to trigonometric form:

In Fig 1, and are acute angles and

As

Hence,

Replacing *B *by *-B* in *i)*

Also from the diagram:

Hence,

Also:

We have derived the compound angle formulae above.

All the compound angle formulas are listed below:

#### Double Angle formulae

We use compound angle formulas from above to find double angle formula i.e

If:

Replacing *B by A*:

Similar replace *B by A*:

Finally,

#### Example #1

Q. Given that , where is obtuse, find the exact value of

i) sin 2

ii) cos 2

iii)tan 2

Solution:

As

By pythagoras theorem

So, now we know and (minus sign because theta is in the second quadrant and cos & tan are negative in the second quadrant)

i)

*Ans:*

ii)

*Ans:*

iii)

*Ans:*

**Function**

Suppose a function , where *a* and *b* are constants, it can be easily converted into a single trigonometric function of the form where R is a positive constant and is an acute angle.

#### Example #2

If we have a function:

We equate it with its trigonometric form:

Expand the right hand side:

Compare the coefficients of and :

To find R we take the magnitude of 7 and 24

To find we do:

°

*Ans: *Hence the trigonometric form is °