Question

Найти tg2х, если tg х = -2,4 и х – угол II четверти.

Answer 1

$tg2x=\frac{2tgx}{1-tg^2x}$

$tg2x=\frac{2(-2.4)}{1-(-2.4)^2}=\frac{-4.8}{1-5.76}=\frac{4.8}{4.76}$

 

Answer 2

Finding the value of tg(2x) given tg(x) = -2.4 and x is an angle in the second quadrant

To find the value of tg(2x), we need to use the trigonometric identity for the tangent of double angles:

tg(2x) = (2 * tg(x)) / (1 - tg^2(x))

Given that tg(x) = -2.4 and x is an angle in the second quadrant, we can substitute these values into the formula to find tg(2x).

Substituting tg(x) = -2.4 into the formula, we get:

tg(2x) = (2 * (-2.4)) / (1 - (-2.4)^2)

Simplifying further:

tg(2x) = (-4.8) / (1 - 5.76)

tg(2x) = (-4.8) / (-4.76)

tg(2x) ≈ 1.008403

Therefore, the approximate value of tg(2x) is 1.008403.

Please note that the above calculation is based on the given information and the trigonometric identity for the tangent of double angles.