Understanding the Half Angle Formulas

The half-angle formulas can be used to reduce the power of a squared trig function.

The half-angle formulas are:







Examples: Rewrite each expression to contain only first-degree functions:

1)

We must use the formula to reduce the power. Notice that 45° is





We could stop here, but if you remember that we can go further:



2)

We must use the formula to reduce the power. Notice that is





3)

We aren't told what equals in this expression, so we will work with it as is. Let's replace



And since they have the same denominator we can subtract the numerators:



Next we'll distribute and combine like terms:





And reduce:



Practice: Rewrite each expression to contain only first-degree trig functions

1)

2)

3)

4)

5)

Answers:1) 2) 3) 4) 5)

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