A-Level Maths | Trigonometry

• Year 12 Trig Identities
  • sin(x)/cos(x) = tan(x)
  • sin²(x) + cos²(x) = 1
• Radians
  • 180 degrees = pi radians
  • 360 degrees = 2 pi radians
  • 90 degrees = 1/2 pi radians
  • To convert degrees to radians: divide by 180 and times by pi
  • To convert radians to degrees: divide by pi and times by 180
• sec(x), cosec(x) and cot(x)
  • sec(x) = 1/cos(x)
  • cosec(x) = 1/ sin(x)
  • cot(x) = 1/tan(x)

Question 1

Question 2

• Pythagorean Identities
  • S = I + T
  • sec²(x) = 1 + tan²(x)
  • cosec²(x) = 1 + cot²(x)

Question 3

Question 4

• Compound angles
• Given in formula booklet
  • sin(A+B) = sinAcosB + cosAsinB
  • cos(A+B) = cosAcosB - sinAsinB
• If one sign changes e.g. + to = then all the signs change
• To derive sin(2A), work out sin(A+A) and cos(2A) would be cos(A+A)
  • sin(2A) = 2sinAcosA
  • cos(2A) =
    • 1 - 2sin²A
    • 2cos²A - 1
    • cos²(A) - sin²(A)

Question 5

Question 6

Question 7

• R-Transformations
  • R² = A² + B²
  • tan(α) = B/A

Question 8

Question 9

Question 10