Extending Trig Functions [10/05/07]

r= Radius

r= √x²+y²

SINΘ= y/r

COSΘ= x/r

TANΘ= y/x

CSCΘ= r/y

SECθ= r/x

COTθ= x/y

*Obviously, x,y,r≠0 because 1) you can't divide by 0, and 2) you can't have a 0° angle in a triangle because, well, then it wouldn't be triangle, would it?

Example:

P (-2,3) Find all six trig functions.

r= √2²+3²
r= √4+9
r= √13

SINΘ= 3/√13

COSΘ= -2/√13

TANΘ= 3/-2

CSCΘ= √13/3

SECΘ= √13/-2

COTΘ= √-2/3

*At this point, Truitt asked, "What exactly are we finding with the functions?"

Jenna answered, "We find theta (θ)."

Marchetti enlightened us further.

Quadrant I= All positive

Quadrant II= SIN +

Quadrant III= TAN+

Quandrant IV= COS+

*The reciprocal functions will be positive at the same time their original functions are.

*"All Star Trig Class"

...A: all positive in quadrant I, S: SIN positive in quadrant II, T: TAN positive in quadrant III, C: COS positive in quadrant IV.

Quadrantal Angles:

→Big word for "angle that takes up entire quadrant"
→Class nicknamed quadrantal angles 'Steve' for some reason...

→Angles begin and end on any axis

Unit circle: r=1

So...

Reference Angles:

→An angle formed by the terminal side of an angle in standard position and the horizontal (x) axis.
→Are our friends.

Homework:

→Unit Circle handout
→Revisions
→p424: 1-55 odd