Question

tan(sin^-1(-5/13))

Answer 1

assume sin^-1(5/13) = A
sin A = 5/13
find cos A by using
cos A = Sqrt(1 - sin^2(A))
then insert in tan A = sin A / cos A
you will get tan A
tan A is nothing but tan(sin^-1(-5/13))

Answer 2

This is just a calculator issue. You don't know how to do this on your calculator.
Every calculator is different
Basically, just find the inverse sin key (sin^-1) and find the inverse sin of -5/13.
Then take the answer to that and find the tan.
All of this work is done on your calculator.

Answer 3

this has nothing to do with calculators

Answer 4

there is a picture of an angle whose sine is \(\frac{5}{13}\)
find the missing side via pythagoras, it is
\[5^2+a^2=13^2\] and so \(a=12\)

Answer 5

It could be done on a calculator.
But I can see where you're going too.
You are right. This particular one can be done without one.

Answer 6

you want the tangent of that angle, which is "opposite over adjacent" i.e. \(\frac{5}{12}\) but now you have to be careful about the minus sign in the question

Answer 7

\[\sin^{-1}(-\frac{5}{13})=\theta\implies \sin(\theta)=-\frac{5}{13}\] so you are in quadrant 4
that means tangent it negative

Answer 8

Calculator or no calculator?
When you have to give an exact answer, put away the calculator!
In this case, surely an exact answer is needed.
It is all about manipulating a bit with the given numbers and some well-known formulas (or at least, formulas that should be well-known).
If you do this with a calculator, you only get an approximation and have no fun at all in finding this "answer".

In my class, students often ask: how is it possible you know how to do this?
My answer is: because I know all these "well-known" formulas...
All they have to do is to learn a few of these, to make life far more easier.
Still, maybe only half of them are prepared to do so.