February 8, 2010 MATH FUN

A link that I found helpful and summed up the identities that I also listed below:http://www.sosmath.com/trig/Trig5/trig5/trig5.html

Today we started out with a warm-up which tested our knowledge of the basic trig functions. If you would like to practice this at home it is on the blog.

Next we chatted about patterns:
Sin
0 0˚ 0 Think of them as square roots, and remember: COS is the same exact backwards...
π/6 30˚ 1/2
π/4 45˚ √2/2
π/3 60˚ √3/2
π/2 90˚ 1---- think of it as √4/2

ALSO: tan π/6=√3/3 tanπ/4=1 tanπ/3=√3

1/√3 and √3/3 are the same thing just rationalized

Remember:
Quad I- sin θ + Quad I-A
cos θ +
tan θ +
Quad 2- sin θ + Quad II-S
Quad 3- tan θ + Quad III-T
Quad 4- cos θ + Quad IV-C
A fun way to remember this is All Students Take Calculus

The reference angle- is an acute angle formed by the terminal side x-axis

To solve things such as cot(150˚), look to the reference angle, which is 30˚. Think of the quadrant it is in and you get cot150˚=-cot30˚=-1/tan30˚=-1/1/√3= -√3

Another good tip other than funny form of one is: -3/√3=-√9/√3=-√9/3=-√3

Identities:
Reciprocal: sinθ=1/cscθ cscθ=1/sinθ
cos θ=1/secθ secθ=1/cosθ
tanθ=1/cotθ cotθ=1/tanθ

Quotient: tanθ=sinθ/cosθ
cotθ= cosθ/sinθ

Co-Function: sinθ=cos((π/2)-θ)
cosθ=sin((π/2)-θ)
secθ=csc((π/2)-θ)
cscθ=sec((π/2)-θ)
tanθ=cot((π/2)-θ)
cotθ=tan((π/2)-θ)

Pythagorean: sin²θ+cos²θ=1 then divide both sides by a sin²θ
which makes it: 1+cot²θ=csc²θ
and also: 1+tan²θ=sec²θ

After taking some vigorous notes we then went over the quiz from last time.

HW: Look on the ical and also we have a QUIZ next class

On my mind: I need to memorize. I feel like there are a lot of patterns but I just need to find time to put them all together and really make sense of the patterns.