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Pre-Calc Exam Notes 25

Pre-Calc Exam Notes 25 - Trigonometric Functions of Any...

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Trigonometric Functions of Any Angle Section 1.4 25 We can now define the trigonometric functions of any angle in terms of Cartesian coor- dinates . Recall that the xy -coordinate plane consists of points denoted by pairs ( x , y ) of real numbers. The first number, x , is the point’s x coordinate , and the second number, y , is its y coordinate . The x and y coordinates are measured by their positions along the x -axis and y -axis , respectively, which determine the point’s position in the plane. This divides the xy -coordinate plane into four quadrants (denoted by QI, QII, QIII, QIV), based on the signs of x and y (see Figure 1.4.3(a)-(b)). x y 0 QI x > 0 y > 0 QII x < 0 y > 0 QIII x < 0 y < 0 QIV x > 0 y < 0 (a) Quadrants I-IV x y 0 (2 , 3) ( 3 , 2) ( 2 , 2) (3 , 3) (b) Points in the plane x y 0 θ r ( x , y ) (c) Angle θ in the plane Figure 1.4.3 xy -coordinate plane Now let θ be any angle. We say that θ is in standard position
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