Question

If sin x = 1/4
and pi < x < 3pi/2 , find tan x exactly.​

Answer 1

Answer:

This problem is impossible.

Step-by-step explanation:

$\sin x$ is negative when $\pi<x<\frac{3\pi}2$

Answer 2

Answer:

Step-b

You need to remember that the tangent function is rational, hence tan 2x = (sin 2x)/(cos 2x).

The problem provides the information that the angle x is in quadrant 3, hence sin xlt0 ; cos xlt 0 .

You need to remember the formula of half of angle such that:

sin x = sqrt((1-cos 2x)/2)

Substituting -1/3  for sin x yields:

-1/3 = sqrt((1-cos 2x)/2)

You need to raise to square to remove the square root such that:

1/9 = (1-cos 2x)/2 =gt 2/9 = 1 - cos 2x

cos 2x = 1 - 2/9 =gt cos 2x = 7/9

You need to use the basic formula of trigonometry to find sin 2x such that:

sin 2x = sqrt(1 - cos^2 2x)

sin 2x = sqrt(1 - 49/81) =gt sin 2x = sqrt(32/81)

sin 2x = sqrt32/9

You need to substitute sqrt32/9  for sin 2x  and 7/9  for cos 2x  in tan 2x = (sin 2x)/(cos 2x)  such that:

tan 2x = (sqrt32/9)/(7/9) =gt tan 2x = (sqrt32/9)*(9/7)

tan 2x = sqrt32/7

Hence, evaluating the tangent of double of angle x yields tan 2x = sqrt32/7.

y-

step explanation:

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