1. A person is observing the moon, which is 238,860 miles away. The moon has a diameter of 2160 miles. What is the angle in degrees spanned (think diameter) by the moon in the eye of the beholder?
(4 points)
The angle [pic] is in the first quadrant of the unit circle and [pic]. Since [pic], does this mean that [pic]and [pic]? If not, clearly explain and give the exact values of [pic]and [pic].
Yes, [pic], does in fact mean that [pic]and [pic] because the tangent function is generally defined in terms of the (x, y) coordinates of the point P on the unit circle.
(4 points)
|[pic] |
|[pic] |
3. Consider the equation [pic] for [pic]. Using graphs, explain/show why this equation:
(8 points)
a. has one solution for k = 3.
* The equation has one solution at this k value because it is the Maximum value of the equation within the given domain of [pic].
b. has two solutions for k = -1/2.
* The equation has two solutions at this k value because the equation decreases at one point of (.848, -1/2) and increases at (2.29, -1/2) within the given domain of [pic].
c. has three solutions for k = 1.
* The equation has three solutions at this k value because the equation begins to increase at one point of (-3.14, 1) and then decreases at (0, 1) and then increases again at (3.14, 1) in which it completes it’s cycle within the given domain of [pic]. The k = 1 value also pertains to the equation’s midline within the given domain.
d. has no solutions for k = -2.
* The equation has no solutions at this k value because the...