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38 Cards in this Set
- Front
- Back
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Find Cos t, t=0 |
1 |
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Find Sin t, t=0 |
0 |
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Find Tan t, t=0 |
0 |
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Find CSC t, t=0 |
Undefined, because sine/y = 0 and you can't divide by 0 |
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Find Sec t, t=0 |
1 |
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Find Cot t, t=0 |
Undefined, because sine/y = 0 and you can't divide by 0 |
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Sin π/6 |
1/2 |
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Cos π/6 |
√3/2 |
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Tan π/6 |
√3/3 |
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Sin π/3 |
√3/2 |
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Cos π/3 |
1/2 |
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Tan π/3 |
√3 |
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Quadrant II Angles |
2π/3 3π/4 5π/6 |
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Quadrant III Angles |
7π/6 5π/4 4π/3 |
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Quadrant IV Angles |
5π/3 7π/4 11π/6 |
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Law of Sin: Sin A ÷ a = Sin B÷b = Sin C ÷ c |
Used when at least: the opposite sidelength or angle measure is known (e.g. b/B) and an established side AND angle are known (e.g. Sin A/a) |
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Law of Cos: a^2 = b^2 + c^2 − (2bcCosA) |
Used when two adjacents and one opposite angle are known. To find the angle with Law of Cos take the ArcSin of: /_A = (b^2 + c^2 - a^2) ÷ (2bc) |
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tan^2 θ + 1 = sec^2 θ |
1 + cot^2 θ = csc^2 θ |
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Even / Odd Identities of sin, cos, tan |
sin(-x) = -sin x cos(-x) = cos x tan(-x) = -tan x |
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sin(s+t) sin(s-t) |
sin(s+t) = sin(s)cos(t)+cos(s)sin(t) sin(s-t) = sin(s)cos(t)-cos(s)sin(t) ("sin/cos/cos/sin", operational signs match!) |
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cos(s+t) cos(s-t) |
cos(s+t) = cos(s)cos(t)-sin(s)sin(t) cos(s-t) = cos(s)cos(t)+sin(s)sin(t) ("cos/cos/sin/sin" operational signs OPPOSITE!) |
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tan(s+t) tan(s-t) |
tan(s+t) = [tan s + tan t] ÷ [1 - tan(s)⋅tan(t)] tan(s-t) = [tan s - tan t] ÷ [1 + tan(s)⋅tan(t)] |
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Sin^-1 / ArcSin |
Domain [-1,1] Range [-π/2, π/2] |
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Cos^-1 / ArcCos |
Domain [-1,1] Range [0,π] |
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Tan^-1 / ArcTan |
Domain: ℝ Range [-π/2, π/2] |
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Graph of arccot |
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Graph of arcsec |
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Graph of sec x |
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Graph of CSC x |
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Graph of arccsc x |
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Area Formula |
A = 1/2ab(sin θ) |
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Heron's Formula |
A = √s(s-a)(s-b)(s-c) s = 1/2 (a+b+c) |
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Cofunction identities |
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Double Angle for Sine (sin 2x) |
Sin 2x = 2sin(x)cos(x) |
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Double Angle for Cosine (cos 2x) |
Cos 2x = (cos^2x)-(sin^2 x) OR Cos 2x = 1-2sin^2(x) OR Cos 2x = 2cos^2(x)-1 |
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Double Angle for Tangent (tan 2x) |
tan 2x = (2tan(x)) ÷ (1-tan^2(x)) |
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Lowering Powers |
Sin^2(θ) = (1-cos2θ)/2 cos^2(θ) = (1+cos2θ )/2 tan^2(θ) = (1-cos2θ)/(1+cos2θ ) |
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Half - Angle Formulas |
sin (u/2) = +/- √[(1-cosu)/2] cos (u/2) = +/= √[(1+cosu)/2] tan (u/2) = (1-cos u)/(sin u) = (sin u)/(1+cos u) |
