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Further Trigonometry

Further Trigonometry. Learning Outcomes Calculate distances and angles in solids using plane sections and trig ratios Be able to sketch graphs of sine, cosine and tangent functions Use sine (including the ambiguous case) and cosine rules to solve problems, including simple cases in 3D

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Further Trigonometry

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  1. Further Trigonometry • Learning Outcomes • Calculate distances and angles in solids using plane sections and trig ratios • Be able to sketch graphs of sine, cosine and tangent functions • Use sine (including the ambiguous case) and cosine rules to solve problems, including simple cases in 3D • Be able to use ½absinC to calculate the area of a triangle

  2. Further Trig Pythagoras’ Theorem & 3D Trig Consider the cuboid below • Find: • The length of the diagonal DG • The length of the diagonal FD • The angle the line FD makes with the base DCGH

  3. x 4 7 Further Trig Revision of Trig & Pythagoras Find x on the following right angled triangles. 3. 1. 2. x 10 10 5 x 5 3 6. 4. 5. 4 7. x x 25º 30º 3.2 15 10 3 7.5 x x

  4. B a c A b C Further Trig Sine Rule For a side For an angle

  5. B 9 8 A b C Further Trig Sine Rule Find angle C. ? 50º

  6. Further Trig Sine Rule Find the length of AC. A 62º 76º B ? 9 42º C

  7. B a c A C b Further Trig Cosine Rule Use with non right angled triangles a2 = b2 + c2 – 2bc cos A

  8. Further Trig Cosine Rule A 105º 8.1 5.2 x C B B 11.4 4.8 x A C 8.5

  9. Further Trig Additional Notes

  10. Further Trigonometry Learning Outcomes: At the end of the topic I will be able to Can Revise Do Further • Calculate distances and angles in solids using plane sections and trig ratios • Be able to sketch graphs of sine, cosine and tangent functions • Use sine (including the ambiguous case) and cosine rules to solve problems, including simple cases in 3D • Be able to use ½absinC to calculate the area of a triangle        

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