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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 xo opposite adjacent hypotenuse yo

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**Consider a circle of radius 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. y 1 Q2 Q1 y = sin xo 90o 180o 270o 360o xo Q3 Q4 -1 Q1 Q2 Q3 Q4

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**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 Q2 Q3 Q4 Q1

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**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 y = tan 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

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Trigonometry Section 7.4 Find the sine and cosine of special angles. Consider the angles 20 o and 160 o Note: sin 20 o = sin160 o and cos 20 o = -cos 160.

Trigonometry Section 7.4 Find the sine and cosine of special angles. Consider the angles 20 o and 160 o Note: sin 20 o = sin160 o and cos 20 o = -cos 160.

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