Today In Math

ok, for my wld lit blog assingment we have to create 4 more entries, this of course is the first of my 4.

SO, today or rather this week, in math class we are starting a new chapter, chapter 7 Analytic Trigonometry. Sounds fun, right? Oh, and for those of you who did not know i am in algebra II/trig this year.
wicked smart, right?
well..no, more like wicked dumb but, that's a diff story.

7.1 USING FUNDAMENTAL IDENTITES

in this chapter (which i still have to do the homework for XP) is about applying the fundamental trigonometric identites(obviously) to problems given to us. There are 5 different types of identites:
Reciprocal Identites:
sin u = 1/csc u cos u = 1/sec u tan u = 1/cot u

csc u = 1/sin u sec u = 1/cos u cot u = 1/tan u

*tip~the only change between these is just making the second set of equations the inverse of the first, which is pretty much what csc, sec, & cot are, the inverses of sin, cos, & tan.

Quotient Identites:
tan u = sin u/cos u cot u = cos u/sin u

*tip~once again the only thing to catch here is that its just the tan equation in inverse form using cot.

Pythagorean Identities:
sin^2 u + cos^2 u = 1 1 + tan^2 u = sec^2 u 1 = cot^2 u = csc^2 u

*fyi~for those who do not know or remember ^ means exponent, in this case ^2 means squared. sin=sine cos=cosine tan=tangent csc=cosecant sec=secant cot=cotangent

Cofunction Identities:
sin(pi/2-u) = cos u cos(pi/2-u) = sin u

tan(pi/2-u) = cot u cot(pi/2-u) = tan u

sec(pi/2-u) = csc u csc(pi/2-u) =sec u

*fyi~pi is 3.141592654...etc
*tip~inverses

Even/Odd Identities:
sin(-u) = -sin u cos(-u) = cos u tan(-u) = -tan u

csc(-u) = -csc u sec(-u) = sec u cot(-u) = -cot u

*tip~guess what?...inverses!

ex. 1
simplifying a trigonometric expression

sin x cos^2 x-sin x

sin x cos^2 x-sin x= sin x(cos^2 x -1) monomial factor
=-sin x(1- cos^2 x) factor out -1
=-sin x(sin^2 x) pythagorean i.d.
=-sin^3 x multiply

ex.2
factoring trigonomrtic expressions

csc^2 x - cot x - 3

csc^2 x - cot x - 3 = (1 + cot^2 x) - cot x - 3 pythagorean i.d.
= cot^2 x - cot x - 2 combine like terms
= (cot x - 2) ( cot x + 1) factor