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In this booklet we review the definition of these trigonometric ratios and extend the concept of cosine, sine and tangent. We define the cosine, sine and tangent as functions of all real numbers. These trigonometric functions are extremely important in science, engineering and mathematics, and some familiarity with them will be assumed in most
Trigonometry: a study of triangles, with emphasis on calculation involving the links of size and the measures of angles. Law of signs: equations relating the sines of the interior angles of a triangle and the corresponding
TRIGONOMETRY Right Triangle Definitions Circular Definitions Other Identities sin cos tan sec csc opp adj hyp hyp opp adj cot adj opp hyp hyp adj opp θθ θθ θθ == == == sin cos tan sec csc yx rr yx cot x y rr x y θθ θθ θθ = = = = = = sin cos tan cot cos sin 11 sec csc cos sin x x xx x x xx x x == == Reduction Formulas Sum and ...
USEFUL TRIGONOMETRIC IDENTITIES Unit circle properties cos(ˇ x) = cos(x) sin(ˇ x) = sin(x) tan(ˇ x) = tan(x) cos(ˇ+x) = cos(x) sin(ˇ+x) = sin(x) tan(ˇ+x) = tan(x)
One of the simplest and most basic formulas in Trigonometry provides the measure of an arc in terms of the radius of the circle, N, and the arc’s central angle θ, expressed in radians. The formula is easily derived from the portion of the circumference subtended by θ.
unit circle and the trigonometric definitions of sine, cosine and tangent. It does not discuss the connection between the geometric and unit circle definitions, as that is more appropriate for a formal geometry course. The chapter ends with other properties of trig functions, including the reciprocal functions. 3
The sine, cosine and tangent of an angle are all defined in terms of trigonometry, but they can also be expressed as functions. In this unit we examine these functions and their graphs.
