You can put this solution on YOUR website! This can be done using a calculator but you have to know how and even then you will only get a decimal approximation of the exact answer.
We can do this without calculators fortunately. sin-1(3/4) represents an angle whose sin is 3/4. Let's draw a picture of such an angle. (Note: the drawing is not to scale.)
A is the angle whose sin is 3/4. Note how the opposite side is 3 and the hypotenuse is 4. This makes the sin 3/4! To find the sec of A we need the adjacent side, x. To find x we can use the Pythogorean Theorem:
Sec is hypotenuse over adjacent so
sec(sin-1(3/4) =
This is the exact answer. But normally we do not leave square roots in denominators so we will multiply the numerator and denominator by :
sec(sin-1(3/4) =
sec(sin-1(3/4) =
which is the exact answer with a rational denominator.
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