Alan

You don't - you use asin (press the 2nd button  to see it).

If I type asin(0.5), say into the Math Input here, you see sin^-1(0.5):

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}^{\!\!\mathtt{-1}}{\left({\mathtt{0.5}}\right)} = {\mathtt{30^{\circ}}}$$

No.  The sin function must have values between ±1.  213/8 is much bigger than 1!!!

Presumably h(x) = -2x² + 3x -1 and you want to evaluate h(-3).  If so then replace the x's by -3:

h(-3) = -2*(-3)² + 3*(-3) -1

        = -2*9 -9 -1

        = -18 -9 -1

        = -28

What function rules? What table?  

You'll need to give us a bit more background information if we are to make sense of what you are asking.

tangent is opposite/adjacent, so tan(angle)=150/100

$${\mathtt{angle}} = \underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{150}}}{{\mathtt{100}}}}\right)} \Rightarrow {\mathtt{angle}} = {\mathtt{56.309\: \!932\: \!474\: \!02^{\circ}}}$$

No. A 3d vector must always have 3 components.  You just have to leave it in terms of unknown values when you don't have them.  For example, if a2 = -3 and b2 = 7, the third component must be written as -3b3-7a3.

Might be able to give a more satisfactory answer if I saw the question you are trying to answer in its entirety.

It depends what you mean by "don't have".  If you mean these are zero then a2b3 - a3b2 is zero.  If they are just unknown, you can't give that term a value.  

Length of v is √( (-2)² + 0² + 1²) = √(4+0+1) = √5 

$${\sqrt{{\mathtt{5}}}} = {\mathtt{2.236\: \!067\: \!977\: \!499\: \!789\: \!7}}$$

If the last part is meant to be the length of the vector sum of u and v, then you have to sum the components first, before calculating the length, not add the lengths of the individual vectors together.

u+v = (-1, 2, 4)

length of u+v = √( (-1)² + 2² + 4²) = √21

$${\sqrt{{\mathtt{21}}}} = {\mathtt{4.582\: \!575\: \!694\: \!955\: \!84}}$$

oops! forget that!!!

I assume you have a function that's probably fx) = x² - 2x + 3 and you have to evaluate it at x = 1/2.  In which case you have written it down ok, so you just need to complete it:

(1/2)*(1/2) - 2*(1/2) + 3 = 1/4 -1 +3 = 1/4 + 2 = $$2\frac{1}{4}$$