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Trigonometry Flashcards

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2092352077Right Triangle Def. sin θ =Opposite/Hypotenuse0
2092352078Right Triangle Def. cos θ =Adjacent/Hypotenuse1
2092352079Right Triangle Def. tan θ =Opposite/Adjacent2
2092352080Right Triangle Def. csc θ =Hypotenuse/Opposite3
2092352081Right Triangle Def. sec θ =Hypotenuse/Adjacent4
2092352082Right Triangle Def. cot θ =Adjacent/Opposite5
2092352083Unit Circle Def. sin θ =y/1 = y6
2092352084Unit Circle Def. cos θ =x/1 = x7
2092352085Unit Circle Def. tan θ =y/x8
2092352086csc θ =1/y9
2092352087sec θ =1/x10
2092352088cot θ =x/y11
2092352089DomainAll the values of θ that can be plugged into the function.12
2092352090Domain of sinθAny Angle13
2092352091Domain of cosθAny Angle14
2092352092Domain of tanθ≠(n+1/2)π, n=0,±1,±2...15
2092352093Domain of secθ≠(n+1/2)π, n=0,±1,±2...16
2092352094Domain of cscθ≠nπ, n=0,±1,±2...17
2092352095Domain of cotθ≠nπ, n=0,±1,±2...18
2092355184RangeAll possible values to get out of the function19
2092355185Range of values for sin-1≤sinθ≤120
2092355186Range of values for cos-1≤cosθ≤121
2092355187Range of values for tan-∞22
2092355188Range of values for csccscθ≥1 and cscθ≤-123
2092355189Range of values for secsecθ≥1 and secθ≤-124
2092355190Range of values for cot-∞25
2092357756PeriodThe number, T, of a function such that f(θ+T) = f(θ). So if w is a fixed number and θ is any angle we have a period such as sin(wθ) → T=(2π/w)26
2092357757Period of sin(wθ)T = 2π/w27
2092357758Period of cos(wθ)T = 2π/w28
2092357759Period of tan(wθ)T = π/w29
2092357760Period of csc(wθ)T = 2π/w30
2092357761Period of sec(wθ)T = 2π/231
2092357762Period of cot(wθ)T = π/w32
2098578655Identity tanθsinθ/cosθ33
2098578656Identity cotθcosθ/sinθ34
2098578657Reciprocal identity csc θ =1/sinθ35
2098578658Reciprocal Identity sin θ =1/ cscθ36
2098578659Reciprocal Identity sec θ =1/ cosθ37
2098578660Reciprocal Identity cos θ =1/ secθ38
2098578661Reciprocal Identity cot θ =1/ tanθ39
2098578662Reciprocal Identity tan θ =1/ cotθ40
2098578663Pythagorean Identity (sin^2)θ + (cos^2)θ =141
2098578664Pythagorean Identity (tan^2)θ + 1 =(sec^2)θ42
2098578665Pythagorean Identity 1 + (cot^2)θ =(csc^2)θ43
2098578666Even/Odd Formulas sin(-θ) =-sinθ44
2098578667Even/Odd Formulas cos(-θ) =cosθ45
2098578668Even/Odd Formulas tan(-θ) =-tanθ46
2098578669Even/Odd Formulas csc(-θ) =-cscθ47
2098578670Even/Odd Formulas sec(-θ) =secθ48
2098578671Even/Odd Formulas cot(-θ) =-cotθ49
2098578672Periodic Formulas sin(θ + 2πn) =sinθ50
2098578673Periodic Formulas cos(θ + 2πn) =cosθ51
2098578674Periodic Formulas tan(θ + 2πn) =tanθ52
2098578675Periodic Formulas csc(θ + 2πn) =cscθ53
2098578676Periodic Formulas sec(θ + 2πn) =secθ54
2098578677Periodic Formulas cot(θ + πn) =cotθ55
2098578678Double Angle Formulas sin(2θ) =2sinθcosθ56
2098578679Double Angle Formulas cos(2θ) =(cos^2)θ - (sin^2)θ = 2(cos^2)θ - 1 = 1-2(sin^2)θ57
2098578680Double Angle Formulas tan(2θ)=(2tanθ)/(1-(tan^2)θ58
2098578681Radians to Degrees formula x = degrees t = radiansDegrees = 180(radians)/π59
2098578682Degrees to Radians formula x = degrees t = radiansRadians = [π(degrees)]/18060
2098578683Half Angle Formulas (sin^2)θ =(1/2) (1-cos(2θ))61
2098578684Half Angle Formulas (cos^2)θ =(1/2) (1+cos(2θ))62
2098578685Half Angle Formula (tan^2)θ =(1-cos(2θ))/(1+cos(2θ))63
2098578686Sum and Difference Formulas sin (α±β)=(sinα*cosβ) ± (cosα*sinβ)64
2098578687Sum and Difference Formulas cos (α±β)=(cosα*cosβ) ± (sinα*sinβ)65
2098578688Sum and Difference Formulas tan (α±β)=(tanα ± tanβ)/(1±(tanα*tanβ)66
2098578689Product to Sum Formulas (sinα*sinβ) =(1/2)[cos(α-β) - cos(α+β)]67
2098578690Product to Sum Formulas (cosα*cosβ) =(1/2)[cos(α-β)+cos(α±β)]68
2098578691Product to Sum Formulas (sinα*cosβ) =(1/2)[sin(α+β)+sin(α-β)]69
2098578692Product to Sum Formulas (cosα*sinβ) =(1/2)[sin(α+β)-sin(α-β)]70
2098578693Sum to Product Formulas sinα+sinβ2sin[(α+β)/2] * cos[(α-β)/2]71
2098578694Sum to Product Formulas sinα-sinβ2cos[(α+β)/2] * sin[(α-β)/2]72
2098578695Sum to Product Formulas cosα + cosβ2cos[(α+β)/2] * cos[(α-β)/2]73
2098578696Sum to Product Formulas cosα - cosβ2sin[(α+β)/2] * sin[(α-β)/2]74
2098578697Cofunction Formulas sin[(π/2)-θ] =cosθ75
2098578698Cofunction Formulas cos[(π/2)-θ] =sinθ76
2098578699Cofunction Formulas csc[(π/2)-θ] =secθ77
2098578700Cofunction Formulas sec[(π/2)-θ] =cscθ78
2098578701Cofunction Formulas tan[(π/2)-θ] =cotθ79
2098578702Cofunction Formulas cot[(π/2)-θ] =tanθ80

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