How do you evaluate #cos(arcsin (1/4))#?
By the fact that
Next note that
It's also possible to solve this problem by drawing a right triangle, labeling one of the non-right angles as
Less formal style of solution
arcsin of some value gives you the angle that was used derive the that value of the sine
The value given can be used in conjunction with the properties of sine to determine a related triangle.
From this and using Pythagoras we can determine the length of the adjacent.