Trigonometric Identities Flashcards
(23 cards)
Law of sines
a/sinA = b/sinB = c/sinC
Law of cosines
a^2 = b^2 + c^2 - 2bc cosA
Point slope
(y - y_1) = m(x - x_1)
Local extrema theorem
Degree n, at most n-1 relative min/max
Points of inflection theorem
degree n, n >= 2, at most n-2 inflection points. Odd degree at least 1 point inflection.
Binomial theorem
(a+b)^n, n = pascals triangle row left -> right, order n 0, n-1 1, n-2 2, n-3 3
Number line method
Test points above or below zero
Rational functions/polynomial long division
Q=Quotient, D=Divider, R=Remainder. Quotient + Remainder/Divider
X and Y intercepts
f(x) = P(x)/Q(x). P(x)=0 for x intercept in numerator. f(0) for y intercept in both
Vertical asymptotes (denominator)
f(x) = P(x)/Q(x), Q(x) = 0, but P(x) NOT = 0
Holes (both)
Factor. Numbers same in both = holes at x coordinates. Take them both out. Plug in x coordinate. Find and plot (x, y).
End behavior <
n < m, horizontal asymptote y = 0
End behavior =
n = m, horizontal asymptote y = a/b
End behavior >
n > m, no horizontal asymptote. Polynomial long division, Quotient = slant asymptote.
Polar -> rectangular
x = rcosθ, y = rsinθ
Period
Period = 2π/b
Pythagoran trigomometric identities
sin^2θ + cos^2θ = 1, find others by dividing by sin^2θ and cos^2θ
Sum identities
sin(a+b)=sinacosb + sinbcosa
cos(a+b)=cosacosb - sinasinb
Difference identities
sin(a-b)=sinacosb - sinbcosa
cos(a-b)=cosacosb + sinasinb
Double angle identities (sin)
sin(2a) = sin (a+a) = 2sinacosa
Double angle identities (cos)
cos(2a) = cos (a+a) = cos^2a - sin^2a
cos(2a) = cos (a+a) = 1 - 2sin^2a
cos(2a) = cos (a+a) = 2cos^2a - 1
Rectangular -> polar
r = √(x² + y²)
θ = tan^-1/arctan(y/x) if x > 0, add π if x < 0 - must find correct quadrant and adjust
Complex Numbers
a + bi -> r( cosθ + isinθ )
