“cos(-.084806) and that equals 0.661437828 radians.” is the correct numerical value, but the cos of an angle is a ratio without units, not measured in radians.

Bear in mind that there are two angles that have a sine of -3/4 as in the picture, but the range of the Arcsin is in the first and fourth quadrants:

http://s236.photobucket.com/albums/ff177/jsardi56/?action=view¤t=cosarcsine10-7-7.jpg

The -3/4 can be thought of as two sides of a right triangle. The third side can be found by the Pythagorean theorem √[4^2 – 3^2] = √(16 – 9) = √7

So your answer is exactly (√7)/4

Also, if your calculator was in degree mode, your intermediate result would have been -48.59 degrees.

arcsin(-3/4) = -0.848062079

so now your expression is cos(-.084806) and that equals 0.661437828 radians.