(a) Construct a MATLAB function M-file called theta.m, that takes as input the time t≥) (possibly an array of time values), and gives as output the corresponding value(s) of θ(t). your M-file will be of the following form:

% Your names, project name, date

function y=theta(t)

% A function to output the angle theta at any input time t.

% Should allow for the possibility that the input is an array

x = 15*cos(pi*t);

% alpha is angle OAB

alpha = atan(x/8);

% beta is angle BAP

beta =

y= pi - (alpha + beta);

Fill in the blank to complete this function M-file correctly.

(b) Create a similar function M-file called phi.m, that calculates the angle φ(t) given t.

(c) Your project report must include

• your derivation of the missing formula for the angle beta, and
• your derivaion of a formula for φ(t).