How do you input arccos

Since this calculator cannot perform symbolic manipulations (algebra) you never need to type in sin(theta) or cos(theta). To calculate the sine of an angle (whatever the name of the angle may be) just press the sin key followed by an angle value and the function will be calculated. same thing with any other trigonometric function.
Make sure that the angle units is set to the unit required by your calculation: degree, radian, or grad.

{r, theta} is equivalent to r*exp(i*theta)=r*cos(theta) +i*sin(theta)
That is all you need.

You have several types of graphs
Function graphs
Y_1=f(x), Y1=3X^2-4, [X, T, Theta, n] key types X
Polar graphs r=F(theta), r=r_o*ln(theta). [X, T, Theta, n] types Theta
Parametric graphs X_1=f(T) and Y_1=g(T). [X.T, Theta, n] types T
Examples: X_1= cos(T). Y_1= 2(1--sin(T))
Sequence graphs u_n+1= f(u_n), [X,T,Theta,n] types n

You have several types of graphs
Function graphs
Y_1=f(x), Y1=3X^2-4, [X, T, Theta, n] key types X
Polar graphs r=F(theta), r=r_o*ln(theta). [X, T, Theta, n] types Theta
Parametric graphs X_1=f(T) and Y_1=g(T). [X.T, Theta, n] types T
Examples: X_1= cos(T). Y_1= 2(1--sin(T))
Sequence graphs u_n+1= f(u_n), [X,T,Theta,n] types n

Shift sin 0.0454, and square you answer

See image below

When using trigonometric functions (cos, sin, tan) and their inverses (arccos, arcsin, arctan) one must be aware that the result will depend on the default angle unit : radian, degree, or grad.

Apparently you are working with the degree as the angle unit, so you must configure the calculator for that unit. (See screen capture below)
Press [SHIFT][MODE] [3:Deg]

we can represent 5 sin X --3 cos X as

5.83 sin ( X - 30.96)

if you want steps please leave a comment and don't forget to vote for me thank you

This is a trigonometry problem not a calculator's.
cos(x) +tan(x).sin(x) = ( cos(x) + (sin(x)/cos(x)).sin(x). After reduction to the same denominator (which is cos(x)) you obtain

{cos(x).cos(x) + sin(x).sin(x)} divided by cos(x).
The content of the bracket above is just 1.
Your fraction will have 1 as numerator and cos(x) as denomitor. That is exactly the definition of the secant function i.e. Function sec is the reciprocal (not the inverse) of the cos function, while the arccos is the inverse of cos.

A mild advice: Avoid writing function without specifying the argument (the variable on which a function acts).

Note:

Hello,
The e is the same, it is the exponential. According to Euler's relation
e^(i theta) = cos(theta) + i sin(theta), where i is the imaginary unit.
When represented on the complex plane (x,iy) the point (cos(theta), sin(theta)) is at the extremity of a vector of length 1 and making an angle theta with the real axis.

In (plane) polar coordinates, a point is defined by the radius r, and the angle, theta, it makes with the x axis, measured in the trigonometric (counterclockwise) direction. It is structurally equaivalent to representing it in the complex plane as r*e^(i*theta). Since r is the measure ot is radius, and the theta is it argument (angle). The complex notation is used for its convenience when adding vectors (as is AC circuits)
That is the theory.
I am inserting a clipping from the book to show you how to convert between polar and rectangular coordinates.