## Trigonometry (10th Edition)

No, there does not exist an angle with the function values $\cos$$\theta = \frac{2}{3} and \sin$$\theta$ = $\frac{3}{4}$.
Using the Trigonometric Identity $\sin$$^{2} \theta + \cos$$^{2}$ $\theta$ = 1 we can determine if this is true. $\sin$$^{2} \theta + \cos$$^{2}$ $\theta$ = ($\frac{3}{4}$)$^{2}$ + ($\frac{2}{3}$)$^{2}$ = ($\frac{9}{16}$) + ($\frac{4}{9}$) = $\frac{145}{144}$ $\frac{145}{144}$ $\ne$ 1 Since the trigonometric identity has been not been satisfied the angle does not exist.