4-2: Pythagorean, Reciprocal, and Quotient Properties

Although I happened to not be in class on the day of this lecture (due to a tennis match... in which we lost), a fellow classmate aka Madison, took amazing notes. Nonetheless, I will provide you all with an awesome blog.

This section basically introduces you to a bunch of basic property formulas... (no need for calculators!)




These three types of properties (reciprocal, quotient & Pythagorean) express relationships among trigonometric functions, in other words, they show that 2 different-looking things are actually the same.



Reciprocal Properties (everyone should already know these by heart, but just in case you don't...)

• sin x = 1 / csc x
• cos x = 1 / sec x
• tan x = 1 / cot x

Quotient Properties

• tan x = ( sin x / cos x) = ( sec x / csc x )
• A simple memory trick= the S's (sin & sec) stay on top

• cot x = ( cos x / sin x ) = ( csc x / sec x)

Pythagorean Properties:

http://img171.imageshack.us/img171/4269/dfadfoi7.png ::: a unit circle drawing that corresponds to these properties...

• Pythagorean identity: sin^2 x + cos^2 x = 1
• sin^2 x = leg
• cos ^2 x = leg
• 1 = hypotenuse (radius)

This equation can be used to derive the following equations:

• sin^2 x + cos^2 x = 1
• Divide everything by sin^2 x. --> (sin^2 x / sin^2 x) + (cos^2 x / sin^2 x) = (1 / sin^2 x)
• 1 + cot^2 x = csc^2 x

• sin^2 x + cos^2 x = 1
• Divide everything by cos^2 x. --> (sin^2 x / cos^2 x) + (cos^2 x / cos^2 x) = (1 / cos^2 x)
• tan^2 x + 1 = sec^2 x

• 1 = sin^2 x + cos^2 x
• Substract cos^2 x from both sides.
• 1 - cos^2 x = sin^2 x

• 1 = sin^2x + cos^2 x
• Substract sin^2 x from both sides.
• 1 - sin^2 x = cos^2 x

~El Fin~

Reminder for Joey(ballgame) to post next... (I'm guessing, after Nick.)

Well, since my computer and blogger.com decided to hate me tonight, I couldn't upload any images. Here is a website that basically has everything I have in this post, but neater and easier to read

***http://www.gomath.com/htdocs/ToGoSheet/Trigonometric/properties.html***.

And for some laughs... I found these pretty funny "solutions" to some simple math problems. Sorry for the inconvenience of having a million links, everyone...

1. http://img218.imageshack.us/img218/2562/sdffii9.png

2. http://img226.imageshack.us/img226/1466/dddig4.png

3. HILARIOUS TO THE MAX!!! Notice how the student "expands". http://img218.imageshack.us/img218/3293/cvrg5.png