Question

Suppose sin(x) = -3/5 and cos(x) < 0. What the value of cos(2x)? -16/25-7/257/2516/25

Answer 1

We have that:

$\sin (x)=-\frac{3}{5}$

And with this information, we need to find the value of cos(2x).

To do this we use the following formula that relates sinx and cos(2x):

$\cos (2x)=1-2\sin ^2x$

Substituting the value of sin(x):

$\cos 2x=1-2(-\frac{3}{5})^2$

Now we need to solve the operations. We squared (-3/5) and we get (9/25):

$\cos (2x)=1-2(\frac{9}{25})$

Next, we multiply 2 by (9/25) and get 18/25 instead:

$\cos (2x)=1-\frac{18}{25}$

And finally, to make this substraction we consider 1=25/25

$\begin{gathered} \cos (2x)=\frac{25}{25}-\frac{18}{25} \\ \cos (2x)=\frac{7}{25} \end{gathered}$

But, since we are considering that cos(x)<0 (is negative), then cos(2x) must also be negative, so the answer is:

$-\frac{7}{25}$