Question

А-угол IV четверти.Найдите tg a ,если cos a =2/7

Answer 1

Ответ:

3√5

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2

Пошаговое объяснение:

фото с решением прилагается

Answer 2

To find the tangent (tg) of angle "a," we can use the trigonometric identity:

$\tan(a) = \frac{{\sin(a)}}{{\cos(a)}}$

To calculate the value of $\sin(a)$, we can use the Pythagorean identity:

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

Given $\cos(a) = \frac{2}{7}$, we can find $\sin(a)$:

$\sin^2(a) + \left(\frac{2}{7}\right)^2 = 1$ $\sin^2(a) + \frac{4}{49} = 1$ $\sin^2(a) = 1 - \frac{4}{49}$ $\sin^2(a) = \frac{45}{49}$ $\sin(a) = \pm \frac{\sqrt{45}}{7}$

Since we are in the IV quadrant, both sine and tangent will be negative.

$\sin(a) = -\frac{\sqrt{45}}{7}$

Now we can calculate the tangent:

$\tan(a) = \frac{\sin(a)}{\cos(a)}$ $\tan(a) = \frac{-\frac{\sqrt{45}}{7}}{\frac{2}{7}}$ $\tan(a) = \frac{-\sqrt{45}}{2}$

So, the value of $\tan(a)$ in the IV quadrant, given $\cos(a) = \frac{2}{7}$, is $\frac{-\sqrt{45}}{2}$.