how do I use a calculator to solve the given trig ratio to find indicated trig ratio.
sin=0.6116,sec I know the answer is sec=1.264,but how do I do it.

What you can do is to find the value of the angle first.

Press SHIFT (or 2nd Function) and press SIN, followed by the value of sin x.

[By the way, you must say sin x, or sin\theta because sin on its own does not have any value.]

This should show as:

sin^{-1}(0.6166)

Press enter or '=' and you should get a value, that's the angle.

Then, you know that \sec\theta = \frac{1}{cos\theta}

So, press COS ANS to get the value of the function. This should give you 0.7911...

Now, press 1\div ANS to give you 1.2639... = 1.264

Is it okay? :)