Question

If cos(x) = Negative one-fourth and tan(x) < 0, what is sin(2x) ? Negative StartFraction StartRoot 15 EndRoot Over 4 EndFraction Negative StartFraction StartRoot 15 EndRoot Over 8 EndFraction StartFraction StartRoot 15 EndRoot Over 8 EndFraction StartFraction StartRoot 15 EndRoot Over 4 EndFraction

Answer 1

Answer:

B. -15 square root / 8

Step-by-step explanation:

EDG2020

Answer 2

The value of sin(2x) is $\sin(2x) = - \frac{\sqrt{15}}{8}$

How to determine the value of sin(2x)

The cosine ratio is given as:

$\cos(x) = -\frac 14$

Calculate sine(x) using the following identity equation

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

So we have:

$\sin^2(x) + (1/4)^2 = 1$

$\sin^2(x) + 1/16= 1$

Subtract 1/16 from both sides

$\sin^2(x) = 15/16$

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

$\sin(x) = \sqrt{15}/4$

sin(2x) is then calculated as:

$\sin(2x) = 2\sin(x)\cos(x)$

So, we have:

$\sin(2x) = -2 * \frac{\sqrt{15}}{4} * \frac 14$

This gives

$\sin(2x) = - \frac{\sqrt{15}}{8}$

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