Trigonometry

Traps in Trigonometry

• Careless calculation
  Not a knowledge gap — a checking gap. Re-read the question, estimate the answer first, and check every line before you choose an option.
• Confuses sin, cos and tan
  SOH CAH TOA: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent. Label the sides relative to the angle FIRST, then choose the ratio.
• Sign slip when moving or multiplying terms
  Moving a term across "=" means doing the opposite operation to BOTH sides. And (−)×(−) = (+). Write each step on a new line; circle every minus sign before you expand.
• Multiplies where it should divide (or vice versa)
  Write the ratio with the unknown in place (tan θ = opposite/adjacent → adjacent = opposite ÷ tan θ) and rearrange before using the calculator.
• Calculates a different quantity
  Name the quantity and its unit before you start (remainder; horizontal distance; cm²). After calculating, check your number is that quantity and not a neighbour.
• Repeats a given value as the answer
  If your answer equals a number in the question, check whether the rule really leaves it unchanged. Most rules transform the given value.
• Applies the rule for a different situation
  Identify the situation first (angle at centre? opposite angles of a cyclic quadrilateral? reverse bearing?) and write the rule that belongs to it before calculating.
• Uses the wrong operation
  Write the rule in words first (bearing back = bearing ± 180°; IQR = Q₃ − Q₁), then substitute. Estimate: does the size of the answer make sense?
• Swaps two things that must stay in order
  Keep order explicit: (x, y); 'bearing of Q from P' starts at P; in p → q the condition comes first. Label each part before you write the answer.