Question 1162249
Find the exact values of sin(2θ), cos(2θ), and tan(2θ) when sin θ =-7/12 and 180∘ < 𝜃 < 270∘.
<pre>The other person who responded gave you WRONG answers. The problem asks for EXACT VALUES. What he gave you are NOT exact values!
{{{matrix(1,7, sin (theta), "=", (- 7)/12, "=", O/H, "=", y/r)}}}. We then need to find A, or x, which will be negative, since {{{theta}}} is an &#8736 in the 3rd quadrant (180∘ < 𝜃 < 270∘).
{{{matrix(5,3, x^2, "=", r^2 - y^2,
x^2, "=", 12^2 - (- 7)^2,
x^2, "=", 144 - 49,
x^2, "=", 95,
x, "=", - sqrt(95))}}}
Therefore, THREE of the 6 TRIG. RATIOS are: {{{system(matrix(1,7, sin (theta), "=", (- 7)/12, "=", O/H, "=", y/r), matrix(1,7, cos (theta), "=", A/H, "=", x/r, "=", (- sqrt(95))/12), matrix(1,9, tan (theta), "=", O/A, "=", y/x, "=", (- 7)/(- sqrt(95)), "=", 7sqrt(95)/95))}}}
You may not need tan 𝜃, depending on which formula you use. 
For me, since I would've determined sin 2𝜃 and cos 2𝜃, I would then use the formula: {{{matrix(1,3, tan (2theta), "=", sin (2theta)/cos (2theta))}}}. Then again, you decide!!

Below, I've done {{{sin (2theta)}}} for you. Follow that same concept to determine cos 2𝜃 and maybe tan 2𝜃.
{{{matrix(1,3, sin (2theta), "=", 2 sin (theta) cos (theta))}}}
{{{matrix(1,5, sin (2theta), "=", 2((- 7)/12), "*", (- sqrt(95))/12)}}} ------ Substituting {{{(- 7)/12}}}, for, sin 𝜃, and {{{(- sqrt(95))/12}}} for cos 𝜃. 
{{{highlight_green(matrix(1,7, sin (2theta), "=", (- 7)/6, "*", (- sqrt(95))/12, "=", highlight(7sqrt(95)/72)))}}}
BTW, Edwin, your tan 𝜃 is WRONG!!