Please answer hesee questions nicely , I have an assignment due today and it would be really helpful

Q7 (10 points) Find the exact value of the following numbers. 1. sin(arccos()) 2. arccos(sin( 1x ))Q8 (10 points) Solve the following equation for x: 2 tan(x) sec- (x) W / N = V3Q9 (10 points) Suppose you find a small tree in the forest. By observing the tree throughout time and gathering data, you find that the number of branches the tree has at a given time f, in years, is modeled by the equation 150 - 2 Bit) = ead" 2' + 50 How old will the tree be when it obtains 50 branches? Approximate your answer to the nearest integer. Q10 (10 points) The electric field of an electromagnetic plane wave traveling in a single direction can be modeled using a cosine function of the form E(x, t) = Ep cos(kx wt) +C where Eo, k, @ and C are constants, and x and are variables that represent position and time, respectively. Let us fix as a reference point x = 25 in space in order to analyze how the electric field changes throughout time at this point. By taking different values, we find that the electric field reaches its first maximum value of E = 1500 when t = 20 and its first minimum value of EF = 250 whent = 120. Find the values of Ep, k, @ and C that fit this data. Q5 (10 points) Consider the function f(x) = In(x? + 2). The graph of f is given below. | 1. Based on the graph, explain why the inverse of this function exists. 2. Find explicitly f! (x). 3. Sketch the graph of f~