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Trigonometry

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

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xoxo y 90 o 180 o 270 o 360 o 1 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. Q1Q1 Q4Q4 Q3Q3 Q2Q2 Q1Q1 Q2Q2 Q3Q3 Q4Q4 y = sin x o

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y = cos x o y = tan x o Q2Q2 Q3Q3 Q4Q4 Q1Q1 Notice that in Q 1 all the curves are positive – that is, they have a y-value greater than 0. In the other three quadrants, only one curve is positive – the other two are negative: y = sin x o is positive in Q2. y = tan x o is positive in Q3. y = cos x o is positive in Q4. This is summarised by the CAST acronym:

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

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