Respuesta :
Simplify the equation to obain the value of x.
[tex]\begin{gathered} \sin x=\frac{4}{5} \\ x=\sin ^{-1}(\frac{4}{5}) \\ =53.130 \\ =180-53.130 \\ =126.87 \end{gathered}[/tex]So value of x is 126.87, for x lies in second quadrant.
Determine the value of sin 2x.
[tex]\begin{gathered} \sin (2\cdot126.87)=\sin (253.74) \\ =-0.96 \end{gathered}[/tex]Determine the value of cos 2x.
[tex]\begin{gathered} \cos (2\cdot126.87)=\cos 253.74 \\ =-0.2799 \\ \approx-0.28 \end{gathered}[/tex]Determine the value of tan 2x.
[tex]\begin{gathered} \tan (2\cdot126.87)=\tan (253.7) \\ =3.4286 \\ \approx3.43 \end{gathered}[/tex]By using formula:
In second quadrant cos and tan have negative values.
Determine the value of sin 2x by using formula.
[tex]\begin{gathered} \sin 2x=2\sin x\cos x \\ =2\sin x\cdot(-\sqrt[]{1-\sin ^2x}) \\ =-2\cdot\frac{4}{5}\cdot\sqrt[]{1-(\frac{4}{5})^2} \\ =-\frac{8}{5}\cdot\sqrt[]{\frac{25-16}{25}} \\ =-\frac{8}{5}\cdot\frac{3}{5} \\ =-\frac{24}{25} \\ =-0.96 \end{gathered}[/tex]Determine the value of cos 2x by using formula.
[tex]\begin{gathered} \cos 2x=1-2\sin ^2x \\ =1-2\cdot(\frac{4}{5})^2 \\ =1-\frac{32}{25} \\ =-\frac{7}{25} \\ =-0.28 \end{gathered}[/tex]Determine the value of tan 2x by using formula.
[tex]\begin{gathered} \tan 2x=\frac{\sin 2x}{\cos 2x} \\ =-\frac{0.96}{-0.28} \\ =3.4285 \\ \approx3.43 \end{gathered}[/tex]So values of the expressions are,
sin 2x = -0.96
cos 2x = -0.28
tan 2x = 3.43
