2nd Hour Pre-Calculus B (Spring 2012): Power-Reducing Formulas, Half-Angle Formulas, Sum-to-Product Formulas, Product-to-Sum Formulas

Power-Reducing Formulas

How to derive the This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

power-reducing formula:

Start out with an formula that includes both cosine and sine

This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

Solve for

First add

to each side. This will cancel it on the right side of the formula. Then you must subtract This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

from each side. Your formula should now look like this:

This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

Now divide each side by 2 and you will get the sine power-reducing formula.

Half-Angle Formulas

How to derive the sine half-angle formula:

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This allows you to substitute u into the equation for theta.

Now your formula should look like:

This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

Take the square root of each side. Remember that the square root of the right side will be This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

The formula should now look like this:

This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

Your final answer can either be + or - but it can not be both! The sign of the final answer depends where it is located on the unit circle.

If you wanted to find This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

you would have to use This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

in the half-angle formula.

Sum-to-Product Formulas

Product-to-Sum Formulas

2nd Hour Pre-Calculus B (Spring 2012)

Thursday, April 5, 2012

Power-Reducing Formulas, Half-Angle Formulas, Sum-to-Product Formulas, Product-to-Sum Formulas

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