Back to . . . . Tom Richmond Bettina Richmond Western Kentucky University 1 Big Red Way Bowling Green, KY 42101 The Sine Curve, Cosine Curve and the Unit Circle NCB Deposit  # 18 For the unit circle . . . .

 The Sine Curve y = Sin(x) where  y is measured in radians To the left of the y-axis, you see a unit circle being swept out, with the radian measure of the angle ( arc length ) shown in blue, and the sine of that angle ( the y-coordinate ) shown in red.  To the right of the y-axis, you see the points of the graph of  y = Sin(x) being graphed in black. The angle x  is shown in blue and the value of Sin(x) is shown in red.

 The Cosine Curve y = Cos(x) To the left of the y-axis, you see a unit circle being swept out, with the radian measure of the angle (arc length) shown in blue, and the cosine of that angle (the x-coordinate) shown in green.  To the right of the y-axis, you see the points of the graph of y = Cos(x) being graphed in black. The angle x is shown in blue and the value of Cos(x) is shown in green.

 Using the graph of f (the sine and cosine functions) as shown above, answer the following: 1.    The value of y =  sin x  at  x  =  0  is  Choose One 0 +1 -1 0.7071 All real numbers All real numbers from -1 to +1 inclusive Odd Even π 2 π 2 Left right . 2.    The value of y =  sin x  at  x  = π/2  is  Choose One 0 +1 -1 0.7071 All real numbers All real numbers from -1 to +1 inclusive Odd Even π 2 π 2 Left Right . 3.    The value of y =  sin x  at  x  = π/4  is  Choose One 0 +1 -1 0.7071 All real numbers All real numbers from -1 to +1 inclusive Odd Even π 2 π 2 Left Right . 4.    The value of y =  sin x  at  x  =  π  is  Choose One 0 +1 -1 0.7071 All real numbers All real numbers from -1 to +1 inclusive Odd Even π 2 π 2 Left Right . 5.    The  maximum value of the function is  Choose One 0 +1 -1 0.7071 All real numbers All real numbers from -1 to +1 inclusive Odd Even π 2 π 2 Left Right . 6.    The  minimum value of the function is  Choose One 0 +1 -1 0.7071 All real numbers All real numbers from -1 to +1 inclusive Odd Even π 2 π 2 Left Right . 7.    The domain of the function is  Choose One 0 +1 -1 0.7071 All real numbers All real numbers from -1 to +1 inclusive Odd Even π 2 π 2 Left Right . 8.    The range of the function is  Choose One 0 +1 -1 0.7071 All real numbers All real numbers from -1 to +1 inclusive Odd Even π 2 π 2 Left Right . 9.    The sine function is an  Choose One 0 +1 -1 0.7071 All real numbers All real numbers from -1 to +1 inclusive Odd Even π 2 π 2 Left Right function as the graph        indicates symmetry with respect to the origin (0,0). 10.  The sine function has a period of  Choose One 0 +1 -1 0.7071 All real numbers All real numbers from -1 to +1 inclusive Odd Even π 2 π 2 Left Right . 11.  The amplitude of y =  sin x  is  Choose One 0 +1 -1 0.7071 All real numbers All real numbers from -1 to +1 inclusive Odd Even π 2 π 2 Left Right .
 Tom and Bettina Richmond have collaborated on several projects.  He is a topologist and she is an algebraist.  See the following publications: The Equal Area Zones Property,  American Mathematical Monthly, Vol.100, No. 5  (May 1993) 475-477. Metric Spaces in Which All Triangles are Degenerate,  American Mathematical Monthly, Vol.104, no. 8 (Oct. 1997) 713-719. Characterizing Power Functions by Volumes of Revolution,  College Mathematics Journal, Vol. 29, no. 1  (Jan. 1998)  40-41. A Discrete Transition to Advanced Mathematics (textbook), Brooks/Cole Series in Advanced Mathematics,  Summer, 2003.