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M119–Precalculus Homework #3–November 13, 2013 1] A regular 12 sided polygon is inscribed in a circle of radius 18 inches. What is its perimeter? What is its area? What is the angle at each vertex? 2] Let u and v be angles in the second quadrant such that sin u = 1/5 and cos v = - 2/5. Find the value of cos (u - v) and sin (u + v). 3] A plane is heading 15 degrees east of north at 180 miles per hour. With what speed is it heading north? 4] The volume of a siren varies periodically between 15 decibels and 35 decibels with a complete cycle lasting 6 seconds. Find a formula for a sine function that models the siren’s volume as a function of time with the highest volume at t = 0 seconds. 5] Making reference to the unit circle explain why tan (-t) = - tan (t) and cos (-t) = cos (t). 6] Why does sin 2 x + cos 2 x = 1 imply that 1 + cot 2 x = csc 2 x ? 7] Why is it always true that *x sin x* # *x*? 8] Find the smallest non-zero solution to asin 2x + sin x = 0 where a = 1//2. 9] How fast is your bicycle moving if its 30 inch diameter tires are making 26 rpm? What rpm would correspond to 30 mph? 10] Find the values of the other trigonometric functions of t if csc t = 5/4 and t is a 2nd quadrant angle. 11] Find the angles in the triangle whose sides have lengths 14, 17, 19. 12] Find the length of the guy wire in figure 1. 13] Identify the missing parts in the triangles in figure 2. 14] What is the exact value of sec (ð/8) ? 15) Convert 27 " 15' to radians and convert 8.2 radians to degrees and minutes. 16] What is the smaller of the two angles between the hour and minute hand at 4:40?