June 2023 Paper 1 Q10

AQACurrent spec8 marksTrigonometry

10 The curve with equation

\[y = \sin x^\circ\]

for \(-360 \leqslant x \leqslant 360\) is shown below.

Graph of y = sin x° from x = −360 to x = 360, with point A marked on the curve above the x-axis between x = −270 and x = −180, and point B marked on the curve just below the x-axis between x = 180 and x = 270
(a) Point \(A\) on the curve has coordinates \((a,\ 0.5)\)
(i) Find the value of \(a\) [2 marks]
(ii) State the value of \(\sin(180^\circ - a^\circ)\) [1 mark]
(b) Point \(B\) on the curve has coordinates \(\left(b,\ -\dfrac{3}{7}\right)\)
(i) Find the exact value of \(\sin(b^\circ - 180^\circ)\) [2 marks]
(ii) Find the exact value of \(\cos b^\circ\) [3 marks]
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