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...
View
Full Document
 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

Click to edit the document details