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Edexcel IAL Mathematics AS P2.6.2 solving trigonometric equations

Edexcel IAL Mathematics AS P2.6.2 solving trigonometric equations
Pearson Edexcel IAL Mathematics syllabusMathematics YMA01First assessment 2019

The direct evidence stresses interval discipline: reduce the equation to sin, cos or tan, solve the algebraic form and list all angles in the required range.

How this is tested

  • Convert equations such as 4tanθ + 5sinθ = 0 into clear sin or cos factors.
  • Solve quadratic forms in sin x or tan 2θ before finding all valid angles.
  • Give answers in the requested interval, with exact radians or rounded degrees as specified.

Question 9

[Maximum number: 3]
Figure 3

Figure 3

Figure 3 shows a sketch of
- the curve with equation y=tan⁡(x−π6)y=\tan \left(x-\frac{\pi}{6}\right) for 0⩽x⩽2π0 \leqslant x \leqslant 2 \pi
- part of the straight line l with equation y=π−xy=\pi-x

Question 9(a)

(a)

State the number of solutions of the equation

[ 3 ]

Question 9(a)(i)

(i)

tan⁡(x−π6)=π−x\tan \left(x-\frac{\pi}{6}\right)=\pi-x in the interval 0⩽x⩽2π0 \leqslant x \leqslant 2 \pi

Question 9(a)(ii)

(ii)

tan⁡(x−π6)=π−x\tan \left(x-\frac{\pi}{6}\right)=\pi-x in the interval 0⩽x⩽100π0 \leqslant x \leqslant 100 \pi

Question 9(a)(iii)

(iii)

tan⁡(x−π6)=π+x\tan\left(x-\frac{\pi}{6}\right)=\pi+x in the interval 0≤x≤2π0\le x\le2\pi

[ 3 ]