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Asked by C.

Hi,I really struggling with trigonometric equations and this is one of the questions I’m stuck on, thank you for any help. Solve sin(2x-60°)=0.5 for 0°≤x≤360°?

Applying arcsin to both sides: 2x - 60 = arcsin(0.5) Rearranging for x: x = 0.5(arcsin(0.5) + 60) arcsin(0.5) = 30 degrees All solutions of x: 45, 225 (= 45 + 180) You can also do this by drawing a y = sin(x) graph, the 2x will mean the graph ‘travels 2 times faster’ i.e will cross 1 at 45 degrees rather than 90. The (- 60) will mean its lagging 60 degrees behind so translate the graph 60 degrees to the left, when it would’ve crossed 1 on the scars graph at 45 degrees, will now cross 1 at -15 degrees.

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Hubert Kaluzny
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