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csc x
peaks at y=1 and y=-1 pi/2 and 3pi/2, NOT intersecting y-axis
sec x
peaks at y=1 and y=-1 and 0, pi, 2pi interSECting y-axis
cot x
slope down, inflection at pi/2 and 3pi/2 opposite of where tan inflection/asymptotes are
sin(x)csc(x)
1 (reciprocals)
cos(x)sec(x)
1 (reciprocals)
Double angle: sin(2x)
2sin(x)cos(x)
Double angle: cos(2x)
cos²(x)-sin²(x) / 2cos²(x)-1 / 1-2sin²(x)
Pythagorean: sin²x + cos²x
1
sin(A+B)
sinA cosB + cosA sinB
sin(A-B)
sinA cosB - cosA sinB
cos(A+B)
cosA cosB - sinA sinB
cos(A-B)
cosA cosB + sinA sinB
tan
sin/cos
cot
cos/sin
period =
2pi/B or pi/B
tan vert asymptotes
≠pi/2 + kpi where k is any integer
polar —> rectangular
x = r cos Ø, y = r sin Ø
rectangular —> polar
x² + y² = r² tanØ = y/x (x ≠ 0)
r pos/increasing
distance from origin increasing
r pos/decreasing
distance from origin decreasing
r neg/increasing
distance from origin decreasing
r neg/decreasing
distance from origin increasing
r = a cos(nØ)
n = odd petals
convex limacon (no loop)
a/b > 2
r = a sin(nØ)
n = even petals
limacon (w/ loop)
a/b < 1
cardioid (butt)
a/b = 1
Circles
radius a // cos, on right tangent to y-axis // sin, top tangent to x-axis