4-2 Pythagorean, Reciprocal, and Quotient Properties

Lesson 4.2

Hey guys so today we learned how to derive algerbraically three kinds of properties expressing relationships among trigonometric functions.

All of these properties make it possible to show how two unlike looking things actually are equal to each other.

Reciprocal Properties:

• Reciprocal properties are just one over cosecant, secant and cotangent to get sin, cos and tan respectively.
  

Quotient Properties:

Pythagorean Properties:

Pythagorean properties are all based off of the first equation listed here. (To find the second equation, we just divided by cos^2. To find the third equation, we just divided by sin^2.)

Example Problem:

Show algebraically how tan x can be transformed into sec x /csc x using the quotient properties.

tan x = sin x / cos x = [(1/ csc x) / (1/sec x)] = sec x / csc x

Extra Help:

For a list of the properties go to: http://www.gomath.com/htdocs/ToGoSheet/Trigonometric/properties.html

For extra explinations go to: http://library.thinkquest.org/20991/alg2/trig.html

Reminder: Ellen you are next!

Haha i want to meet this little girl: