the exact value is
sin(arccos(3/4))The equation for cosine is cos(A)=AdjacentHypotenuse. The inside trig function is arccos(3/4), which means cos(A)=3/4. Comparing cos(A)=AdjacentHypotenuse with cos(A)=3/4, find Adjacent=3 and Hypotenuse=4. Then, using the pythagorean theorem, find Opposite=√7.Adjacent=3Opposite=√7Hypotenuse=4Substitute in the known variables for the equation sin(A)=OppositeHypotenuse.sin(A)=√7 over 4Simplify.√7 over 4
