How to sketch the graph of sine from 0 to 360 degrees

Key concept: The sine graph is one of the easiest full-cycle sketches once you know the anchor points. You do not need a calculator here; the standard angles tell the whole story.

Step by step

To sketch $y=\sin x$ for $0^\circ\le x\le 360^\circ$, mark the key values of sine at the standard angles:

$x$	$\sin x$
$0^\circ$	0
$90^\circ$	1
$180^\circ$	0
$270^\circ$	-1
$360^\circ$	0

Shape of the curve

• Start at $(0,0)$
• Rise smoothly to a maximum at $(90^\circ,1)$
• Cross the axis at $(180^\circ,0)$
• Fall to a minimum at $(270^\circ,-1)$
• Return to $(360^\circ,0)$

The curve should be smooth and wave-like, not piecewise straight. Label the axes clearly, and make sure the peak and trough are at the correct heights.

A neat sketch with these points joined by a smooth sinusoidal curve is the expected graph.

Pitfall alert

Do not plot the sine graph like a zigzag. Another common issue is mixing up sine and cosine: cosine starts at 1, while sine starts at 0. Also remember that the question uses degrees, not radians.

Try different conditions

If the graph were $y=\sin(x+90^\circ)$, it would shift left and match cosine. If the question asked for $y=2\sin x$, the same x-values would stay the same, but the maximum and minimum would become 2 and -2.

Further reading

amplitude, period, unit circle