Step-by-step explanation:
The value of sin(2x) is \sin(2x) = - \frac{\sqrt{15}}{8}sin(2x)=−
8
15
How to determine the value of sin(2x)
The cosine ratio is given as:
\cos(x) = -\frac 14cos(x)=−
4
1
Calculate sine(x) using the following identity equation
\sin^2(x) + \cos^2(x) = 1sin
2
(x)+cos
2
(x)=1
So we have:
\sin^2(x) + (1/4)^2 = 1sin
2
(x)+(1/4)
2
=1
\sin^2(x) + 1/16= 1sin
2
(x)+1/16=1
Subtract 1/16 from both sides
\sin^2(x) = 15/16sin
2
(x)=15/16
Take the square root of both sides
\sin(x) = \pm \sqrt{15/16
Given that
tan(x) < 0
It means that:
sin(x) < 0
So, we have:
\sin(x) = -\sqrt{15/16
Simplify
\sin(x) = \sqrt{15}/4sin(x)=
15
/4
sin(2x) is then calculated as:
\sin(2x) = 2\sin(x)\cos(x)sin(2x)=2sin(x)cos(x)
So, we have:
\sin(2x) = -2 * \frac{\sqrt{15}}{4} * \frac 14sin(2x)=−2∗
4
15
∗
4
1
This gives
\sin(2x) = - \frac{\sqrt{15}}{8}sin(2x)=−
8
15
