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Trigonometry

Trigonometry. hypotenuse. opposite. x o. adjacent. y o. hypotenuse. adjacent. opposite. A review of basic trigonometry. SOH CAH TOA ‘Opposite’ and ‘adjacent’ are defined by the angle that is being considered.

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Trigonometry

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  1. Trigonometry

  2. hypotenuse opposite xo adjacent yo hypotenuse adjacent opposite A review of basic trigonometry SOH CAH TOA ‘Opposite’ and ‘adjacent’ are defined by the angle that is being considered.

  3. Consider a circle of radius 1. If the red line is rotated from its starting point then a series of triangles will be formed – the radius always being the hypotenuse. Given that sinx is defined as the ratio of the opposite side to that of the hypotenuse, the graph of y = sin x can be plotted. y 1 Q2 Q1 y = sin xo 180o 90o 270o 360o xo Q3 Q4 -1 Q2 Q3 Q1 Q4

  4. Q1 Q2 Q3 Q4 Notice that in Q1 all the curves are positive – that is, they have a y-value greater than 0. y = sin xo In the other three quadrants, only one curve is positive – the other two are negative: y = sin xo is positive in Q2. y = tan xo is positive in Q3. y = cos xo is positive in Q4. y = cos xo This is summarised by the CAST acronym: y = tan xo

  5. The solid lines indicate symmetry on the graphs. On the sine graph the y-value at x = 30o will be identical to that at x = 150o. i.e. sin 30o = sin 150o y = sin xo y = cos xo The dashed lines indicate another type of symmetry on the graphs. On the cosine graph the y-value at x = 60o will be the negative of that at x = 120o. i.e. cos 60o = – cos 120o y = tan xo

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