Algebra 2 - Chapter 14 Flashcards
how to find the amplitude of sine and cosine functions (2)
a = |a|
always positive
graph transformations for sine, cosine, tangent, and cotangent functions (how to determine what is a and b)
y = asinbx y = acosbx y = atanbx y = acotbx
how to find the period of sine and cosine functions
P = (2π/ |b|)
- |b| = | b |
what does a indicate?
vertical stretch, if |a| > 1
vertical compression, if 0 < |a| < 1
if a < 0, then the graph is reflected across the x-axis
frequency (3)
number of cycles in a given unit of time
measured in Hertz (Hz) –> 1 cycle / sec.
frequency = 1 /period (= to the reciprocal of the period)
format of the transformations of trig. functions
label variables
y = asinb(x-h)+k
a = amplitude b = period h = phase shift k = vertical shift
rules for phase shift
left = + right = -
how to find the x-intercepts
use phase shift (use based on positive or negative value) and then add nπ, where n is an integer
parent functions for the trig functions
y = ?x
ex. y = sinx, cosx, etc.
when is the tangent function undefined ?
when θ = (π/2) + πn, where n is an integer
how to find the period for tangent and cotangent graphs
P = π / |b|
how to locate the asymptotes for tangent and cotangent graphs
X = [π/2|b|] + [πn/ |b|], where n is an integer
how to find the amplitude for tangent, cotangent, secant and cosecant graphs
amplitude = undefined
trig and reciprocal pairs (3)
sine and cosecant (sine + csc)
cosine and secant (cos + sec)
tangent and cotangent (tan + cot)
Pythagorean theorem in terms of fundamental trig identities (2)
x^2 + y^2 = r^2
(x^2 / r^2) + (y^2 / r^2) = 1
