Trig Identities - Sum and Difference

Today we continued on with the Trig Identities unit and into a section called "Sum and Difference Identities". Today basically consisted of us learning six formulas using sin, cos, and tan; and how to solve angles that we are unfamiliar with, such angles as 7pi/12 and tan(75) (for the formulas, refer to the formula sheet. All these formulas will be given to us on the final exam, so know them, DON'T MEMORIZE THEM). A sum and difference question can be looked at as being a 2 part question. What I mean by two part question is that there is more that one piece to the problem, and furthermore by piece I mean angle. Up until now we were familiar with angles like pi/6, pi/4, pi/3, etc....... and never really thought of having a twelfth of a pi. Now comes the thinking part. "I don't know a thing about pi/12, but since this angle can be thought of as a 2 angle identity, mamby two angles I already know can add up to a twelfth..!!" Now we are on to something, two angle we know are pi/3 and pi/4, and added together equal to 7pi/12. Well that seems pretty easy some would say, but some question will take a little more effort that that to be solved. Unfortunately the only way to come about finding these answers is by educated guessing and checking. Mr Max said that solving identities was like doing a puzzle, so let the puzzle sloving begin. Use the angles you already know on the unit circle and take some previous fractions knowledge, put them together to figure it out. when you find the two angles that add together or subtract from each other, go to the formula sheet and find the corresponding formula. when you have the formula, set one angle to alpha and one to beta, AND DO NOT SWITCH THEM AROUND. Plug the alpha value into everywhere the alpha symbol appears in the formula, and do the same for the beta value. from here all you are solving for now is exact values that come strait off the unit circle. Follow throughout the formula and complete all the algebra taking into consideration the order of operations, and eventually you will end up with an answer. (haha I know, convincing eh??) The trick is practice, and the must is remembering algebra rules.

If you need help ever and don't have a teacher or tutor at your right hand, there is a new sight on the net called wolfram alpha (http://www.wolframalpha.com/). this site virtually lets you type in any mathematical question and it gives you the answer in about 15 different ways, and it can even graph it!! try it out for yourself and see what wolfram can do for you!!! This has been a paid advertisement for wolfram alpha inc. jkjk Mr. Max told me to put it on. so i did....

Anyways, The homework for today was Exercise 16 #1-15, but omit #3 & 5, and remember that there will be a homework check sometime next week on the lessons 11-20.

More Trig Identities

More trig identities, more examples, more fun.
Extraneous Roots is what we're doing today. It is the principle for checking trig identities by substituting your answer into your original equation, either for x or theta. "Sounds good on paper, like communism?" Not all solutions in equation are viable and that's why we do this. So an extraneous root is a solution that we get but doesn't work when checked.
We also did our third mental math today.
No new homework, just work on our old assignment (exercise 15: 1-14)

Trig Identities (more notes, examples,etc..)

Mr. Max says that trig identities is basically the same as solving puzzles in class
there is never the solution only a solution

Techniques to assist proving identities

1.reduce (simplify complicated side to try to "match" the simpler side)

2.work each side independently to some intermediate expression

3. DO the addition / subtraction of the rational expressions.

4.DO the multiplication / division of the same rational expressions.

5. Simplify GCF's ALWAYS (ie. factor if you can)

6. Factor, Factor, Factor

7.try multiplying both numerator / denominator by same expression to get to know identities.

8. IF possible? rewrite all trig. functions as sin(x) or cos (x);look for patterns

Todays assignment is exercise 15 questions 1-14