trigonometry final exam (chapters 7-8)
(a+bi)+(c+di)=
(a+c)+(b+d)i
(a+bi)-(c+di)=
(a-c)+(b-d)i
(a+bi)(c+di)=
(ac-bd)+(ad+bc)i
when are vectors (u and v) orthogonal
when uv=0
how many solutions does a SSA triangle have when the given angle is obtuse
0-1
how many solutions does a SSA triangle have when the given angle is acute
0-2
what type of triangle has a varying number of solutions
SSA
when does vector direction formula change
add pi in Q2/3, add 2pi in Q4
vectors A and B, what is vector AB
c-a,d-b
what law is used to solve an SSS triangle
cosines for largest angle, sines for smaller angle
what law is used to solve an SAS triangle
cosines for remaining side, sines for smaller angle
giving an answer in rectangular form means
evaluating the trig functions
how to divide (a+bi)/(c+di)
multiply the num and denom by the conjugate of the denom
quotient of complex numbers formula (z1/z2)
r1/r2[cos(01-02)+isin(01-02)]
product of complex numbers formula (z1z2)
r1r2[cos(01+02)+isin(01+02)]
powers of complex numbers formula (z^n)
r^n[cos(n0)+isin(n0)]
vector direction formula
tan0=b/a
vector formula
u = a,b
dot product formula (u and v)
u dot v= ac + bd
unit vector formula
u/|u|
angle between two vectors (u and v) formula
uv/|u||v|
(complex numbers) x=
x=rcos0
(complex numbers) y=
y=rsin0
complex number formula in polar form
z=r(cos0+isin0)
complex number formula in rectangular form
z=x+iy
vector magnitude formula
|u|=√a²+b²
imaginary number (i) =
√-1
formula to find a vector, given its magnitude and volume
|u|cos0, |u|sin0