This document discusses trigonometric ratios and functions. It defines the sine, cosine, and tangent ratios for right triangles. It also introduces the reciprocal functions of cosecant, secant, and cotangent. Special angle values for trig functions are provided in a table. The document explains how to write trig functions in terms of x, y, and r using the Cartesian plane and use a CAST diagram to determine the quadrants where trig ratios are positive and negative. Finally, it discusses extending knowledge of special angles using trig ratio definitions in the Cartesian plane.

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5. Trigonometry
Grade 10

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Trigonometric ratios
● We can define three trigonometric ratios for right-angled triangles;
sine (sin), cosine (cos) and tangent (tan):

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Reciprocal functions
● Each of the three trigonometric functions has a reciprocal. The reciprocals,
cosecant (cosec), secant (sec) and cotangent (cot):

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Special angles
● The values of the trigonometric functions for these special angles are listed in the table:

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Trigonometric ratios in
the Cartesian plane
● We can write all the
trigonometric functions in
terms of x, y and r.
● We use the CAST diagram to
determine in which quadrants
the trigonometric ratios are
positive and negative.

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Special angles extended
We can extend our knowledge of special angles using the definitions of the trig ratios in the
Cartesian plane.

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