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TMUA 2020 · Paper 2 · Question 9 of 20

TMUA 2020 Paper 2 Question 9

Trigonometry — Radians and degrees · converting an argument. Try it first; the answer and a full worked solution are below.

TMUA 2020 · Paper 2TrigonometryRadians and degrees · converting an argument6 options
A student wishes to evaluate the function f(x) = xsin x, where x is in radians, but has a calculator that only works in degrees.

What could the student type into their calculator to correctly evaluate f(4)?

  1. A(π × 4 ÷ 180) × sin(4)
  2. B(π × 4 ÷ 180) × sin(π × 4 ÷ 180)
  3. C4 × sin(π × 4 ÷ 180)
  4. D(180 × 4 ÷ π) × sin(4)
  5. E(180 × 4 ÷ π) × sin(180 × 4 ÷ π)
  6. F4 × sin(180 × 4 ÷ π)
Show the answer and worked solution
answer · F
  1. A(π × 4 ÷ 180) × sin(4)
  2. B(π × 4 ÷ 180) × sin(π × 4 ÷ 180)
  3. C4 × sin(π × 4 ÷ 180)
  4. D(180 × 4 ÷ π) × sin(4)
  5. E(180 × 4 ÷ π) × sin(180 × 4 ÷ π)
  6. F4 × sin(180 × 4 ÷ π)
Only the argument of the sine needs converting; the factor of x in front is a plain number and stays as 4. Radians become degrees by multiplying by 180π, so 4 radians is 180 × 4π degrees, which is about 229∘. Hence the student should type 4 × sin(180 × 4 ÷ π). The common wrong turns are converting the multiplier as well, or converting the wrong way with π180.