find the exact value of the expression

Draw a simple sketch of a right angled triangle.



/|
/ |
5 / | 4
/ |
/____|

the sine ratio of the lower left angle is 4/5. Arcsine of that angle gives 4/5

Now, if you are used to the Pythagorean triples (or else, you use the Pythagoras' Theorem), you'll see that the base of this triangle is 3.

sec is the reciprocal of cos. Cos of the angle becomes 3/5 from our drawing.

sec(x) = \frac{1}{cos(x)}

It's nearly done now, can you guess the answer now? :)