Why Does Trig Work? [10/2/07]

Why Does Trig Work?



Triangle Problem:

1.Draw a Trianlge

2.Measure easch side to the nearest 10th of a centimenter

3.Solve for:



AB/AC BC/AC AB/BC

Class Results:

-The actual results are AB/AC = .8192 BC/AC = .5736 AB/BC = 1.4281

It is important to recognize that the ration is constant and that similarity is why trig works

Bearing:

Right Triangle Trig:

SOH CAH TOA :

sin: opp/hyp cos: adj/hyp tan: opp/adj


Reciprocal relationships:

csc: hyp/opp or 1/sin of angle sec: hyp/adj or 1/cos of angle

cot: adj/opp or 1/tan of angle

Ex. :

The sine of an angle equals 5/6 Find values of all 6 trig functions.

Start by using the pythagorean theorem

5^2 + x^2 = 6^2

25 + x^2 = 36

x^2 = 11

x = the square root of 11

Then use SOH CAH TOA to solve for the other 5 trig functions

cos : square root of 11/ 6 sec: 6/square root of 11

tan: 5/square root of 11 cot: square root of 11/ 5

csc: 6/5

Ex. :

Solving a Triangle: Finding all missing pieces

180 - 143 = 37

sin 37 = b/8

b = 8 x sin 37

b= 4.8

cos 37 = a/8

a = 8 x cos 37

a = 6.4


Angle of Depression

30-60-90 Triangle

45-45-90 Triangle

Homework:

pg. 399 1-23 odd 41-55 odd (given on the friday before)

pg. 399 57-73

pg.411 1-23 odd 51-57 odd 71-85 odd


Just for fun, one of my favorite quotes is:

"Twenty years from now you will be more disappointed by the things you didn't do than by the things you did do. So throw off the bowlines. Sail away from the safe harbor. Catch the trade winds in your sails. Explore. Dream. Discover." ~ Mark Twain