Find sin2x, cos2x, and tan2x if cos(x) = 1/sqrt(10) and x terminates in quadrant IV.
+26367 Find sin2x, cos2x, and tan2x if cos(x) = 1/sqrt(10) and x terminates in quadrant IV.
\(\begin{array}{|rcll|} \hline \cos(x) &=& \dfrac{1}{\sqrt{10}} \\ \cos(x) &=& 0.31622776602 \\ x &=& \pm\arccos(0.31622776602) \\ x &=& \pm71.5650511771^\circ \\ x_1 &=& +71.5650511771^\circ \quad | \quad \text{quadrant $I$} \\ \mathbf{x_2} &=& \mathbf{-71.5650511771^\circ} \quad | \quad \text{quadrant $IV$} \\ \hline \end{array}\)
\(\text{$\mathbf{x}$ terminates in quadrant $IV$ and is $\mathbf{-71.5650511771^\circ}$}\)
\(\begin{array}{|rcll|} \hline \sin(2x) &=& \sin\Big(2*(-71.5650511771^\circ)\Big) \\ \sin(2x) &=& \sin (-143.130102354^\circ) \\ \mathbf{\sin(2x)} &=& \mathbf{-0.6} \\ \hline \end{array} \begin{array}{|rcll|} \hline \cos(2x) &=& \cos\Big(2*(-71.5650511771^\circ)\Big) \\ \cos(2x) &=& \cos (-143.130102354^\circ) \\ \mathbf{\cos(2x)} &=& \mathbf{-0.8} \\ \hline \end{array} \)
\(\begin{array}{|rcll|} \hline \tan(2x) &=& \tan\Big(2*(-71.5650511771^\circ)\Big) \\ \tan(2x) &=& \tan (-143.130102354^\circ) \\ \mathbf{\tan(2x)} &=& \mathbf{0.75} \\ \hline \end{array}\)
