Trigonometric functions and circular measure - the Australian ...

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{12} • Trigonometric functions and circular measure3 tan300 ◦ = −tan60 ◦ = − 3y1300 ºO60 º1x4 cos240 ◦ = −cos60 ◦ = − 1 2y1240 º60 ºO1xExercise 3Find the exact value ofa sin210 ◦ b cos315 ◦ c tan150 ◦ .The sine and cosine rulesThe sine ruleIn the module Further trigonometry (Year 10), we introduced and proved the sine rule,which is used to find sides and angles in non-right-angled triangles.In the triangle ABC , labelled as shown, we haveasin A =bsinB =csinC .AcbBaC
A guide for teachers – Years 11 and 12 • {13}Clearly, we may also write this assin Aa= sinBb= sinC .cIn general, one of the three angles may be obtuse. The formula still holds true, althoughthe geometric proof is slightly different.Exercise 4aFind two expressions for h in the diagram below, and hence deduce the sine rule.CahbBPcAbRepeat the method of part (a), using the following diagram, to show that the sine ruleholds in obtuse-angled triangles.ChbaMAcBExampleThe triangle ABC has AB = 9 cm, ∠ABC = 76 ◦ and ∠AC B = 58 ◦ .A9 cmC58 º 76 ºBFind, correct to two decimal places,1 AC 2 BC .
Page 1 and 2: 1Supporting Australian Mathematics
Page 3 and 4: Assumed knowledge . . . . . . . . .
Page 5 and 6: A guide for teachers - Years 11 and
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Trigonometric functions and circular measure - the Australian ...

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