Can anyone help me with the basics of trig used in physics?I'm going into a physics honors class and need help

Question

I only really need a good explanation of the basics of trig because some of the summer assignment for my physics honors class involves trig to solve problems.

Answer 1

There is a GREAT book for you.  It is thin and does not have a lot of "bull".  It is...

Paul A. Foerster's Trigonometry (Functions and Applications) published by Addison-Wesley.  The ISBN (for the 3rd edition) is...0-201-25109-4

Other possibilities for you are the review chapter that is found in most calculus books, like Thomas or Stewart.

Another good guide for you is Schaum's Outline Series (There is one on Trig that any book store can order for you).

You must know...

How to "resolve" a vector into two components, i.e., a force of 100N acts in a direction 30 degrees North of East, find the two components in the North and East directions.  (And you should be able to "go the other way").  

Let's "do" this one, together...

100*cos(30) acts to the North and 100 * sin(30) acts East.

This "addition" of vectors is huge and a very important skill.  

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Let's add a few vectors (put all their "tails" together at the same point)...Always draw a picture!!

One vector (think of it as an arrow) is 50 units long acting at an angle of 45 degrees with the x-axis (45 degrees North of East) and a second acts at 30 degrees West of North with a length of 40 units.  Find the total force.

This is a typical trig question that you would need to solve as part of a physics question.  Put BOTH vecore into components of the x and y axes...

50 at 45 degrees: To the RIGHT 50 cos(45)

UP 50 sin(45)

40 at 30 (Wof N): To the LEFT 40*sin(30)

UP 40 cos (30)

In the North direction: 50 sin(45) + 40 cos (30) = 70 acts UP

East/West: 50 cos(45) - 40 sin(30)= 15.35 (acts right)

We can resolve these into one vector using trig and Pythag's thm:  The magnitude = SQRT(sum of squares) = 71.7 at an angle of...

arctan(70/15.35) = about 78 degrees North of East.

I hope I did nopt make a sign error or some other "muff up", but DO pay attention to WHAT we are doing...that's important!

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To a lesser degree, you should...

Understand...

Sin(x) ^2 + Cos (x) ^2 =1 and its two "sisters"

The double angle relationships are important as well...

sin(2x) = 2sin(x) * cos (x) and

cos(2x) = cos(x) ^2 - sin(x) ^ 2

Knowing how to write a trig relationship involving phase, amplitude, vertical shift, and period is important.

-Fred

Get a copy of the physics book you will be using and see how much trig there really is in the first few chapters.  Ask your teacher for a practice assignment in trig.  (S)he will probably help you "get up to speed".  Most teachers are delighted when their students want to "get a head start".

Go get 'em!!