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AM11 Trigonometry

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AM11 Trigonometry

  1. 1. AM11 TrigonometryAngle (in radians) =Angle (in degrees) = (or in rad) 0° (0 rad) 30° ( rad) 45° ( rad) 60° ( rad) 90° ( rad) sin 0 1 cos 1 0 tan 0 1 undefined Basic angle is θ where 0 < θ < 90° if Angle measured: 1. –θ [4th quadrant] 2. θ [1st quadrant] 3. (180° – θ) [2nd quadrant] 4. (180° + θ) [3rd quadrant] 5. (360°– θ) [4th quadrant] 6. 360n° + any of the 5 –θ 90° – θ 180° – θ 180° + θ 360° – θ 360° + θAngles [4th] [1st] [2nd] [3rd] [4th] [1st] sin – sin θ + cos θ + sin θ – sin θ – sin θ + sin θ cos + cos θ + sin θ – cos θ – cos θ + cos θ + cos θ tan – tan θ + cot θ – tan θ + tan θ – tan θ + tan θ
  2. 2. Equation Graphy = sin x For trigo graphs with y = a sin(bx)+c & y = a cos(bx)+c, 1. Max/min value (amplitude) = a times more 2. No of cycles (frequency) = b times more 3. Period = of original periody = cos x 4. Values on the entire graph = increased by c Range: -1 ≤ sin x ≤1 Amplitude: (Max y – Min y)/2 For trigo graphs with y = tan(bx) + c,y = tan x 1. No of cycles (frequency) = b times more 2. Period = of original period 3. Values on the entire graph = increased by c Amplitude: undefined. cosec θ = , sec θ = , tan θ =
  3. 3. 1. Simple trigonometric identities 1. tan θ = 2. cot θ = 3. sin2 θ + cos2 θ = 1 4. tan2 θ + 1 = sec2 θ 5. cot2 θ + 1 = cosec2 θ2. Addition formulae 1. cos(x – y) = cos x cos y + sin x sin y 2. cos(x + y) = cos x cos y – sin x sin y 3. sin(x – y) = sin x cos y – cos x sin y 4. sin(x + y) = sin x cos y + cos x sin y - 5. tan(x – y) = 6. tan(x + y) = -3. Double angle formulae 1. sin 2x = 2sinxcosx 2. cos 2x = cos2x – sin2x = 2cos2x – 1 = 1 – 2sin2x 3. tan 2x = - 4. *sin x = 5. *cos x = 6. *tan x =
  4. 4. 4. Half angle formulae 1. sin x = 2sin( )cos( ) 2. cos x = cos2( ) – sin2( ) = 2cos2( ) – 1 = 1 – 2sin2( ) 3. tan x = -5. Factor formulae - 1. sin x + sin y = 2sin( )cos( ) - 2. sin x – sin y = 2cos( )sin( ) - 3. cos x + cos y = 2cos( )cos( ) - 4. cos x – cos y = –2sin( )sin( )6. R-formulae 1. a sin θ + b cos θ ≡ R sin(θ + α) 2. a sin θ – b cos θ ≡ R sin(θ – α) 3. a cos θ + b sin θ ≡ R cos(θ – α) 4. a cos θ + b sin θ ≡ R sin(θ + α) R= ,α=

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