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11 Cards in this Set
- Front
- Back
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definition of the unit circle
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y = sinθ
x = cosθ y/x = tanθ x/y = cotθ 1/x = secθ 1/y = cscθ |
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domain - all values of θ that can be used as input in a function
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sinθ: all real numbers
cosθ: all real numbers tanθ: θ != (n+1/2)π cotθ: θ != n(π) secθ: θ != (n+1/2)π cscθ: θ != n(π) |
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range - all possible output values
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-1 <= sinθ <= 1
-1 <= cosθ <= 1 -infinity <= tanθ <= infinity -infinity <= cotθ <= infinity -1 >= secθ >= 1 -1 >= cscθ >= 1 |
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period - number t where f(t + c) = f(t)
or f(θ+T) = f(θ) and w = fixed number |
sin(wθ) T -> T=2π/w
cos(wθ) T -> T=2π/w tan(wθ) T -> T=π/w cot(wθ) T -> T=π/w sec(wθ) T -> T=2π/w csc(wθ) T -> T=2π/w |
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pythagorean identities
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cos*2 θ +sin*2 θ = 1
tan*2 θ +1 = sec*2 θ cot*2 θ + 1 = csc*2 θ |
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even/odd identities
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sin(-θ) = -sinθ
cos(-θ) = cosθ tan(-θ) = -tanθ cot(-θ) = -cotθ sec(-θ) = secθ |
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periodic formula
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sinθ = (θ + 2πn)
cosθ = (θ + 2πn) tanθ = (θ + πn) cotθ = (θ + πn) secθ = ((θ + 2πn) cscθ = (θ + 2πn) |
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double angle formulas
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sin(2θ) = 2sinθcosθ
cos(2θ) = cos*2θ - sin*2θ = 2cos*2θ - 1 = 1 - 2sin*2θ tan(2θ) = 2tanθ --------- 1-tan*2θ |
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even/odd identities
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sin(-θ) = -sinθ
cos(-θ) = cosθ tan(-θ) = -tanθ cot(-θ) = -cotθ sec(-θ) = secθ |
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periodic formula
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sinθ = (θ + 2πn)
cosθ = (θ + 2πn) tanθ = (θ + πn) cotθ = (θ + πn) secθ = ((θ + 2πn) cscθ = (θ + 2πn) |
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double angle formulas
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sin(2θ) = 2sinθcosθ
cos(2θ) = cos*2θ - sin*2θ = 2cos*2θ - 1 = 1 - 2sin*2θ tan(2θ) = 2tanθ --------- 1-tan*2θ |
