Stitz-Zeager_College_Algebra_e-book

# 2 2 sin 1 for 0 2 sin for 0 combine

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Unformatted text preview: ine and cosine are negative (Can you see why?) so we √ conclude sin(θ) = − 2 5 5 . 3. When we substitute sin(θ) = 1 into cos2 (θ) + sin2 (θ) = 1, we ﬁnd cos(θ) = 0. Another tool which helps immensely in determining cosines and sines of angles is the symmetry π inherent in the Unit Circle. Suppose, for instance, we wish to know the cosine and sine of θ = 56 . We plot θ in standard position below and, as usual, let P (x, y ) denote the point on the terminal side of θ which lies on the Unit Circle. Note that the terminal side of θ lies π radians short of one 6 half revolution. In Example 10.2.1, we determined that cos 4 5 π 6 √ = 3 2 This is unfortunate from a ‘function notation’ perspective. See Section 10.6. See Sections 1.1 and 7.2 for details. and sin π 6 = 1 . This means 2 616 Foundations of Trigonometry √ that the point on the terminal side of the angle π , when plotted in standard position, is 23 , 1 . 6 2 From the ﬁgure below, it is clear that the point P (x, y ) we seek can be obtained by reﬂecting that √ π π point about the y -axis. Hence, cos 56 = − 23 and sin 56 = 1 . 2 y y 1 1 θ= P (x, y ) √ 31 ,2 2 √ 5π 6 P− π 6 31 ,2...
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