A-LevelMathematicsDifferentiation9709/33 · Oct/Nov 2022 · Q45 Marks
The parametric equations of a curve are x = 2t - tan t, y = ln(sin 2t), for 0 < t < ½π. Show that dy/dx = cot t.
- The parametric equations of a curve are x = 2t - tan t, y = ln(sin 2t), for 0 < t < ½π. Show that dy/dx = cot t.[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.
- B1 State or imply dx/dt = 2-sec²t or dy/dt = 2 cos 2t / sin 2t
- M1 Use dy/dx = dy/dt ÷ dx/dt
- A1 Obtain correct answer in any form
- M1 Use double angle formula to express derivative in terms of cos x and sin x
- A1 AG Obtain the given answer correctly
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