Pre-Calc Exam Notes 26

Pre-Calc Exam Notes 26 - ◦ ≤ θ< 360 ◦ may fall...

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26 Chapter 1 Right Triangle Trigonometry §1.4 Notice that in the case of an acute angle these deFnitions are equivalent to our earlier deFnitions in terms of right triangles: draw a right triangle with angle θ such that x = adjacent side, y = opposite side, and r = hypotenuse. ±or example, this would give us sin θ = y r = opposite hypotenuse and cos θ = x r = adjacent hypotenuse , just as before (see ±igure 1.4.4(a)). x y 0 θ r hypotenuse ( x , y ) x adjacent side y opposite side (a) Acute angle θ x y 0 QI 0 < θ < 90 QII 90 < θ < 180 QIII 180 < θ < 270 QIV 270 < θ < 360 0 90 180 270 (b) Angles by quadrant Figure 1.4.4 In ±igure 1.4.4(b) we see in which quadrants or on which axes the terminal side of an angle
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Unformatted text preview: ◦ ≤ θ < 360 ◦ may fall. ±rom ±igure 1.4.3(a) and formulas (1.2) and (1.3), we see that we can get negative values for a trigonometric function. ±or example, sin θ < 0 when y < 0. ±igure 1.4.5 summarizes the signs (positive or negative) for the trigonometric functions based on the angle’s quadrant: x y QI sin + cos + tan + csc + sec + cot + QII sin + cos − tan − csc + sec − cot − QIII sin − cos − tan + csc − sec − cot + QIV sin − cos + tan − csc − sec + cot − Figure 1.4.5 Signs of the trigonometric functions by quadrant...
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This note was uploaded on 01/21/2012 for the course MAC 1130 taught by Professor Dr.cheun during the Fall '11 term at FSU.

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