Trigonometry Flashcards
Complementary Identities (p. 468)
Sin(pi/2-theta)=cos(theta)
Csc(pi/2-theta)=sec(theta)
Tan(pi/2-theta)=cot(theta)
Cos(pi/2-theta)=sin(theta)
Sec(pi/2-theta)=csc(theta)
Cot(pi/2-theta)=tan(theta)
Period of function.
Period is 2pi/|B| for functions. If it is a tangent equation it is pi/B.
Wave period
The period of a wave is 360/w where w is the wave function. THis is in the formula y=Acos(wx).
One-to-one function
This is the horizontal line test, basically saying that no y value will happen twice. None of the six trigonometric functions are one to one they repeat.
Complex number to polar form
A+bi—-> z=r(cos(theta)+i*sin(theta)).
Angle in a calculator and what to add for polar form of a complex number.
If you get an angle from doing inverse tan in the 1st quadrant your fine. SEcond quadrant or 3rd quadrant, add 180 degrees, fourth quadrant at 360 degrees.
De Moiv’res formula
(Cos(theta)+isin(theta))^n=cos(n(theta))+isin(n(theta)).
Half angle identities
Sin(1/2 alpha)=+-root(1-cos(alpha)/2)
Cos(1/2alpha)=+-root(1+cos(alpha)/2)
Tan(1/2alpha)=+-root((1-cos(alpha))/(1+cos(alpha))
Double Angle Identities
Sin(2alpha)=2sin(alpha)*cos(alpha)
Cos(2alpha)=cos^2(alpha)sin^2(alpha)=1-2sin^2(alpha)
=2cos^2(alpha)-1.
Tan(2alpha)=2tan(alpha)/(1-tan^2(alpha))
Addition and Subtraction formulas
Sin(a+-b)=sinacosB+-cosasinB
Cos(a+-b)=cosacosb-+sinasinb
Tan(a+-b)=tana+-tanb/(1-+tanatanB)
Graphing trigonometric functions
F(x)=Atrig(BX-C)+D
Trig will just be the generic trig function.
A: Amplitude.
C/B is phase shift.
Vertical shift is D.
Range of Inverse Functions
Arcsin range -pi/2<=y<=pi/2
Arccos range 0<=y<=pi
Arctanx. Range -pi/2 to pi/2
Cartesian coordinate to polar coordinate equation
R=root(a^2+b^2)
Theta=tan^-1(b/a)
