The value of cos x and tan x is less tan x is less than 0, means angle x lies in the second quadrant as in second quadrant cosine and tangent of an angle is negative.
Determine the measure of angle x from the equation cos x = -8/17.

Substitute 118.07 for x in the expression sin 2x to obtain the value of sin 2x.

Thus, value of sin 2x is -0.83.
OR
Determine the value of sin x by using trigonometry identity.
![\begin{gathered} \sin x=\sqrt[]{1-(\cos x)^2} \\ =\sqrt[]{1-(-(8)/(17))^2} \\ =\sqrt[]{(289-64)/(289)} \\ =(15)/(17) \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/po0dqevx3qkn3ntc8n2dipnyhg75legiuj.png)
Determine the value of sin 2x by using trigonometry identity.

So answer is -240/289.