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4-1: RIGHT TRIANGLE TRIGONOMETRY Precalculus Mr. Gallo RIGHT TRIANGLE TRIGONOMETRIC FUNCTIONS Six Trigonometric Functions sine sin opp hyp cosine cos adj hyp tangent tan opp adj cosecant csc secant sec hyp opp Hypotenuse Opposite hyp adj cotangent cot adj opp Adjacent Reciprocal Trigonometric Functions Cosecant, secant and cotangent Ratios are reciprocals of sine, cosine and tangent respectively 1 RIGHT TRIANGLE TRIGONOMETRIC FUNCTIONS Inverse Trigonometric Functions Used to find the measure of an acute angle Hypotenuse Opposite If sin x, then sin x 1 If cos x, then cos 1 x If tan x, then tan 1 x Adjacent ANGLES OF ELEVATION AND DEPRESSION Angle of Elevation The angle above horizontal that an observer must look to see an object that is higher than the observer. It is congruent to the angle of depression. Angle of Depression The angle below horizontal that an observer must look to see an object that is lower than the observer. It is congruent to the angle of elevation. Angle of Depression Angle of Elevation 2 SPECIAL RIGHT TRIANGLES 45° 45° 90° sin 45 x 2 x cos 45 tan x 30° 60° 90° csc 60 2x x 30 x 3 30 45 60 1 2 3 2 3 2 3 3 2 sec 2 3 3 cot 3 2 2 2 1 2 2 1 3 2 2 3 2 2 1 3 3 3 Homework: p.227 #1, 5, 11, 15, 21, 23, 27, 30, 31, 35, 39, 40, 45, 74 3