Answer
Yes, there exists an angle $\theta$ with the functions values $\cos$ = 0.6 and $\sin$ = 0.8.
Work Step by Step
Using the Trigonometric Identity $\sin$$^{2}$ $\theta$ + $\cos$$^{2}$ $\theta$ = 1 we can determine if this is true.
$\sin$$^{2}$ $\theta$ + $\cos$$^{2}$ $\theta$
= (-0.8)$^{2}$ + (0.6)$^{2}$
= (0.64) + (0.36)
= 1.0
Since the trigonometric identity has been satisfied the angle does exist.
