Trigonometric functions and circular measure - the Australian ...

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{36} • Trigonometric functions and circular measurey1y = cos θθ02322–1Symmetries of the sine graphThe graph of y = sinθ has many interesting symmetries.The model employing the unit circle helps to elucidate these. The sine of the angle θ isrepresented by the y-value of the point P on the unit circle. Since sinθ = sin(π − θ), wecan mark two equal intervals on the following sine graph.y1y1y = sin θθ–1θO 1xθθ2θ–1–1θ = 2Hence, between 0 and π, the graph of y = sinθ is symmetric about θ = π 2 .Similarly, between π and 2π, the graph is symmetric about θ = 3π 2 .
A guide for teachers – Years 11 and 12 • {37}y1y1y = sin θ–1+ θO 12 θx+ θ 2 θ2θ–1–1θ = 3 2Finally, the graph possesses a rotational symmetry about θ = π as the following diagramdemonstrates.y1y1y = sin θ–1θO 12 θxθ2 θ2θ–1–1All these observations are summarised by the following diagram. This symmetry diagramillustrates the related angle and the quadrant sign rules, as well as the symmetriesdiscussed above.y1y = sin θθθ+ θ2 θ2θ–1Symmetries of the sine graph.
Page 1 and 2: 1Supporting Australian Mathematics
Page 3 and 4: Assumed knowledge . . . . . . . . .
Page 5 and 6: A guide for teachers - Years 11 and
Page 35: A guide for teachers - Years 11 and
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