1. (12 pts) We defined each trigonometric function two ways. Read them carefully: (i) Cosine of the angle 0 is the x-coordinate of the endpoint of a radius of the unit circle at an angle 0 from the positive horizontal axis. (ii) Given a right triangle with an angle 0, cosine of 0 is the ratio of the adjacent side over the hypotenuse. For the two definitions: (a) Draw and label a diagram, graph, or picture to illustrate each definition. (b) Explain how the two definitions are connected.2. (15 pts) This question is about cosine as a function. (a) What is the domain of cosine? (b) What is the range of cosine? (c) Draw a precise graph of f(x) = cos(x) (axes below, if you need them). Make sure to label the each intercept. -4TT -2TT 0 2TT 4 TT3. (15 pts) The function f(x) = sin(x) doesn't have an inverse unless you restrict its domain. (a) Give an example of a function that DOES have an inverse. What is its inverse? Explain why your function has an inverse. (b) A classmate of yours mistakenly restricted the domain of f (x) = sin(x) to [-n, x] in order to define the inverse function. Why won't this work? Explain.4. (10pts) Recall the identity: cos(x + y) = cos(x) cos(y) - sin(x) sin(y). Use this identity to compute cos(-15). Show all work.5. (15 pts) You win $50,000 on a gameshow and invest it in an account that promises earnings of 4% compounded quarterly. You want to know how many years you have to wait before the account will have $1,000,000 in it. (a) Decide whether the situation is linear or exponential. Explain how you know. (b) Write a function that models this scenario. (c) Sketch the graph of the function from part (b). Make sure to label the axes.6. (15 pts) Without using a calculator, use the table below to compute the following values. (Hint: every input can be written as a product or quotient of the inputs of the logs given in the table.) log (0.001 ) = -3 log(0.28) = -0.553 log (1) = 0 log (5) = 0.699 log(15) = 1.176 log(60) = 1.778 log (400) = 2.602 log(1001 ) = 3.0004 (a) log(15015) (b) log(12) (c) log (0.00028) (d) log(4.2) (e) Solve the equation: log(x) = 0.0004 (Hint: try writing 0.0004 as the sum of two outputs from the table)\f8. (12 pts) You happen to be standing 4,714.64 feet from a very tall building, and you're looking up to the antenna from the ground. For whatever reason, you notice that your line of sight is making a 30 angle with the ground. Make note of all the important information given, and sketch a diagram depicting the sce- nario. Use your diagram to determine how tall this building is. Round to the nearest foot. (2 pts) (Extra Credit) There is a certain famous building with this height. What is the name of this building