Download M119–Precalculus Homework #3–November 13, 2013 1] A regular

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?