Precalculus 3/24/2010

Half Angles Formulas

More Identities. . .

I recommend this one when using tan.

, lies in quadrant III.

Solve for:

Because we are given the tangent we can easily find the cosine-which will help us solve for the problems above.

By using pythagorean we can find the missing side (hypotenuse).

To solve, first find the correct equation to use:

Plug in -15/17 for cosine theta. . .

Make 1=17/17 so that you can add. . .

Next you do same,change, flip. . . multiply the bottom and the top by 1/2 so that you get:

Simplify.

Rationalize the denominator.

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Plug in -15/17 . . .

Like before, make 1= 17/17. . .

Multiply the top and the bottom by 1/2 so that you get. . .

Rationalize the denominator. . .

Tip: Remember to first write out the formula, then draw a picture, and then find the answer to the question .

You can find more notes on Mr. Corn's web page at here

Double Angle Formulas

Here is a list of the formulas you'll need to solve the problems:



*I recommend using this one for cosine








When solving these problems remember these three steps: PICTURE, FORMULA, ANSWER

, Quadrant IV

Find:

Now to solve for sine and cosine were going to use SOH, CAH, TOA to figure out what the sine and cosine of theta is.




*Make sure that you write the equation each time before you start to solve

plug in -4/5 for the sine of theta and 3/5 for cosine and multiply

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plug in -4/5 for your sine


solve for (-4/5) squared



subtract (32/25) from 1, think of one as (25/25) in this case.




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Now you may run into problems that seem like they have nothing to do with what we just went over, but we already know how to solve them. Here's an example...















For all the notes click HERE for a link to Mr. Corn's webpage

New Identities!

This is an example of a Sine addition identity. First you need to split it up (the most important part) and then plug it into the appropriate equation.

Click here for the link to Mr. Corn's page.