146 day 11
November 05, 2014
What is Precalculus? Study of Functions
What's a function? Job
How represented? Data. Graphs. Equations
What equations have we studied?
1. Linear, Quadratic, Polynomial...
2. Rational 3. Exponential
4. Logarithmic
5. Trig Functions!
Wraping Fucntion w(r) or w(θ)
r= radians outside measure of unit circle
θ = degrees
measure of inside angle
146 day 11
November 05, 2014
wraping functions input = angle or radian measure
output = a point on the unit circle
Point (x, y) x= cos (r) or cos (θ)
y = sin (r) or sin ( θ)
y/x = tan (r) or tan (θ)
inverse functions
sin­1(x) means inverse of sine
1/sin(x) = COSECANT = csc(x)
cos­1(x) means inverse of cosine
1/cos(x) = SECANT = sec(x)
tan­1(x) means inverse of tangent
1/tan(x) = COTANGENT = cot(x)
146 day 11
November 05, 2014
Things we know...
Domain
(degrees or radians)
Range
Intercepts, Max/mins
End Behaviour
Asymptotes
Graph
Properties
Transformations
Inverses
146 day 11
November 05, 2014
12+ 29/60 + 57/3600 = 12.499 121dregrees .25*60= 15'
180o
­4π
3
* ­210 * π
π
180
= ­240o
= ­7π
6
146 day 11
November 05, 2014
b) 1170 ­ 3 *360
1170 ­ 1080 = 90 degree
a) ­3pi * 180 = ­108 degrees 5 pi what is coterminal with ­108 degrees?
360 ­ 108 = 252 degree
252 *pi / 180 = 7pi/5 146 day 11
November 05, 2014
s = radius * radians
13 pi/4
146 day 11
November 05, 2014
2d2=64 by pyth so d = √(32) = 4√(2)
14^2=7^2 + x^2 so x = sqroot(147)
196­49=147 = x^2
146 day 11
November 05, 2014
cos(7pi/6)=
=
= ­ 1/2
146 day 11
November 05, 2014
= 1/ tan(5pi/6) = ­ 1.73 = ­
146 day 11
November 05, 2014
1.4142... = .7071... = 146 day 11
November 05, 2014
y = a sin (bx + c) +d
smushed by 2pi/b
shifted left by ­c/b
streched by a
raised by d
146 day 11
November 05, 2014
revered order!
146 day 11
November 05, 2014
146 day 11
November 05, 2014