Quick questions on Trigonometric graphs and equations in degrees for HSC Maths Advanced: the graphs of sine, cosine and tangent over one period, reading amplitude and period from an equation or graph, the wave key points, and solving equations such as 2 cos x = 1 or sin x = -1/2 for all solutions in 0 to 360 degrees using the related acute angle and ASTC.

2short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is the tangent graph?

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Tangent behaves quite differently because

\tan x = \dfrac{\sin x}{\cos x}

. Wherever

\cos x = 0

, at

90\degree

and

270\degree

in the first revolution, the tangent is undefined and the graph shoots up towards a vertical line it never touches, a vertical asymptote. Between the asymptotes the curve rises continuously from far below to far above, passing through

0

wherever

\sin x = 0

, that is at

0\degree

180\degree

and

360\degree

. Because this whole pattern completes in half a revolution, the period of tangent is

180\degree

, not

360\degree

What is calculator left in radian mode?

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A trig answer that is wildly wrong is almost always radians left on. Confirm

\sin 30\degree = 0.5

and keep degrees throughout.

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