Defining Trigonometric Ratios (5.8.1)

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Presentation transcript:

Defining Trigonometric Ratios (5.8.1) June 1st, 2016

*Since all right triangles already have one pair of corresponding angles that are the same, it only takes one more pair of congruent angles to make the triangles similar by AA.

*Since similar triangles have proportional sides, this means that all similar right triangles must have the same side ratios.

*So given a particular side ratio in a triangle, we should be able to determine the acute angle measures of that triangle (given that all similar triangles have the same angle measures).

Trigonometric Ratios The trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) represent the ratios of certain sides of right triangles from the perspective of one of its acute angles. The sides used in each ratio are identified by their position from the angle of perspective, i.e., the side opposite the angle, the side adjacent to the angle, and the hypotenuse of the triangle.

SOH CAH TOA (for trig ratios) Trigonometric Functions -sine of angle : -cosine of angle : -tangent of angle : Reciprocal Trigonometric Functions -cosecant of angle : -secant of angle : -cotangent of angle :

Ex: For the given triangle, set up and calculate each of the following. (a) The trigonometric ratios for the sine, cosine and tangent of . (b) The trigonometric ratios for the cosecant, secant, and cotangent of . (c) The trigonometric ratios for the sine, cosine and tangent of . (d) The trigonometric ratios for the cosecant, secant, and cotangent of .

hypotenuse side opposite side adjacent to

hypotenuse side adjacent to side opposite

Let’s say we knew that . Calculate *How do these answers compare to the corresponding trigonometric ratios of you found in part C? They are the same!!!