Question

Вычислить cos arctg4

Answer 1

tg a =4
Cos a=?
1+( tg a)^2=1/(cos a)^2
Отсюда
Cos a = sqrt(1/17)

Answer 2

Пусть arctg4 = x, тогда tgx = 4.
$1 + {tg}^{2} x = \frac{1}{ {cos}^{2} x}$
Отсюда:
${cos}^{2} x = \frac{1}{1 + {tg}^{2} x} = \frac{1}{1 + 16} = \frac{1}{17} \\ cosx = + - \frac{1}{ \sqrt{17} }$
Но т.к. по определению арктангенс принадлежит 1 и 4 четвертям, где cos > 0, то:

$cosx = \frac{1}{ \sqrt{17} }$

Answer 3

To calculate the value of cos(arctan(4)), we can use the trigonometric identity:

cos(arctan(x)) = 1 / sqrt(1 + x^2)

In this case, x = 4:

cos(arctan(4)) = 1 / sqrt(1 + 4^2) cos(arctan(4)) = 1 / sqrt(1 + 16) cos(arctan(4)) = 1 / sqrt(17)

Now, to get an approximate numerical value, we can evaluate it using a calculator:

cos(arctan(4)) ≈ 0.24253562504

So, the value of cos(arctan(4)) is approximately 0.2425.