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Chapter 6 - Coggle Diagram
Chapter 6
Trig Formulas
(Must be a right triangle)
cosec = hypotenuse / opposite
sec = hypotenuse / adjacent
tanθ = opposite / adjacent
cot = adjacent / opposite
cosθ = adjacent / hypotenuse
arcsinθ = 1 / sinθ
sinθ = opposite / hypotenuse
arccos = 1 / cosθ
arctan = 1/ tanθ
Unit Circle
Non-right triangles
Sine Rule: a/sinA = b/sinB = c/sinC
Cosine Rule: a^2 = b^2 + c^2 - 2(b)(c)(cosA)
SSA or SAA
Shapes
Surface Area
Sphere: 4(pi)(r^2)
Cone: (pi)(r^2) + (pi)(r)(slant height)
Volumes
Sphere: 4/3(pi)(r^3)
Cone: 1/3(pi)(r^2)(h)
Pyramid: 1/3(Abase)(h)
Parts of a circle
Length of an arc = rθ
(radians)
Area of a sector: 1/2(r^2)θ
(radians)
SAA (double angle) Triangles
sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
sin(2A) = 2sin(A)cos(A)
cos(2A)
2cos(2A) - 1
1 - 2cos(2A)
cos^2(A) - sin^2(A)
Calculating points
Midpoint:
Distance:
Trig Functions
y =
a
sin[(
b
(x +
c
)] +
d
c = phase (horizontal) shift
d = vertical shift = (max value
+
min value) / 2
b = 2pi / period
a = amplitude = (max value
-
min value) / 2
