Maths

• integrate sinx


  -cosx + c
• integrate cosx


  sinx + c
• integrate sec^2 x


  tanx + c
• integrate cosecxcotx


  -cosecx + c
• cosec^2 x =


  cot^2 x + 1

  
• sec^2 x =


  tan^2 x + 1

  
• sin^2 x


  (1-cos2x)/2
• cos^2 x


  (1+cos2x)/2
• Integral of 1/x


  ln IxI + C
• Differentiate sin x


  cos x
• Differentiate tan x


  sec² x

  
• Differentiate cot x


  - cosec² x

  
• Differentiate sec x


  sec x tan x
• Differentiate cos x


  - sin x
• Differentiate cosec x


  - cosec x cot x

  
• Differentiate sin 2x


  2 cos 2x
• Differentiate cos 0.5x


  - 0.5 sin 0.5x
• Differentiate sin x cos x

  cos 2x
• Differentiate 2cos0.5x


  -sin0.5x
• Sin2θ


  2sinθcosθ
• When using tan addition formula, watch out for..

  Signs: top and bottom should have opposite signs with the top being the same as the same as the one in the tan(a+-b).
• How do you write a rational number in a proof?

  a/b
• What does y=f(|x|) do?

  Reflects values of x≥0 in the y-axis
• Arithmetic sequence formula


  a₁+(n-1)d
• Geometric sequence formula


  uₙ = arⁿ⁻¹
• Convergent geometric series


  Convergent if |r|<1 where r is the common ratio
• Periodic sequences


  Sequence is periodic if terms repeat in a cycle
• Vectors and angles


  If the vector a = xi + yj + zk makes an angle θₓ with the positive x-axis, then cos(θₓ) = x/(|a|) and similarly for the angles θᵧ and θz.
• Radian to degree conversion

  1 radian = 180°= π
• Arc length


  l=rθ
• Area of a circle sector

  a=1/2 x r²θ
• Arcsin(x) Graph

  
• State the domain of y = arcsinx

  -1 ≤ x ≤ 1
• State the range of y = arcsinx

  -π/2 ≤ y ≤ π/2
• Arccos(x) Graph

  
• State the domain of y = arccosx

  -1 ≤ x ≤ 1
• State the range of y = arccosx

  0 ≤ y ≤ π
• Arctan(x) Graph

  
• State the domain of y = arctanx

  -∞ < x < ∞
• State the range of y = arctanx

  -π/2 < y < π/2