function [sinA,cosA] = approxSinCos(x)
% For a given angle in radians, approximate the sine and cosine of the angle
% using Taylor series.
sinA = x;
cosA = 1;
altSign = -1;
for n = 3:2:26
sinA = sinA + altSign*(x^n)/factorial(n);
cosA = cosA + altSign*(x^(n-1))/factorial(n-1);
altSign = -altSign;
end

%% Test 0rad
% Test expected values of 0
[sinApprox,cosApprox] = approxSinCos(0);
assertWithAbsTol(sinApprox,0)
assertWithRelTol(cosApprox,1)

%% Test 2pi
% Test expected values of 2pi
[sinApprox,cosApprox] = approxSinCos(2*pi);
assertWithAbsTol(sinApprox,0)
assertWithRelTol(cosApprox,1)

%% Test pi over 4 equality
% Test sine and cosine of pi/4 are equal
[sinApprox,cosApprox] = approxSinCos(pi/4);
assertWithRelTol(sinApprox,cosApprox,'sine and cosine should be equal')

%% Test matches MATLAB fcn
% Test values of 2pi/3 match MATLAB output for the sin and cos functions
x = 2*pi/3;
[sinApprox,cosApprox] = approxSinCos(x);
assertWithRelTol(sinApprox,sin(x),'sin does not match')
assertWithRelTol(cosApprox,cos(x),'cos does not match')

function assertWithAbsTol(actVal,expVal,varargin)
% Helper function to assert equality within an absolute tolerance.
% Takes two values and an optional message and compares
% them within an absolute tolerance of 1e-6.
tol = 1e-6;
tf = abs(actVal-expVal) <= tol;
assert(tf, varargin{:});
end

function assertWithRelTol(actVal,expVal,varargin)
% Helper function to assert equality within a relative tolerance.
% Takes two values and an optional message and compares
% them within a relative tolerance of 0.1%.
relTol = 0.001;
tf = abs(expVal - actVal) <= relTol.*abs(expVal);
assert(tf, varargin{:});
end