Stitz-Zeager_College_Algebra_e-book

106 the inverse trigonometric functions 719 integers

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Unformatted text preview: graph of y = cos(x) is usually described as ‘wavelike’ – and indeed, the applications involving the cosine and sine functions feature modeling wavelike phenomena. 5 The use of x and y in this context is not to be confused with the x- and y -coordinates of points on the Unit Circle which define cosine and sine. 674 Foundations of Trigonometry y x An accurately scaled graph of y = cos(x). We can plot the fundamental cycle of the graph of y = sin(x) similarly, with similar results. x 0 sin(x) 0 π 4 π 2 3π 4 2 2 √ 1 2 2 2π 0 √ − 2 2 −1 √ − 2 2 y √ 2 π 4, 2 π 2,1 √ 3π , 22 4 √ π 5π 4 3π 2 7π 4 (x, sin(x)) (0, 0) 1 π 4 (π, 0) √ 2 5π 4 ,− 2 3π 2 , −1 √ 7π , − 22 4 0 π 2 3π 4 π 5π 4 3π 2 7π 4 2π x −1 The ‘fundamental cycle’ of y = sin(x). (2π, 0) As with the graph of y = cos(x), we provide an accurately scaled graph of y = sin(x) below with the fundamental cycle highlighted. y x An accurately scaled graph of y = sin(x). It is no accident that the graphs of y = cos(x) and y = sin(x) are so similar. Using a cofunction identity alo...
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