Question

Найти cos a/2, если cos a= -0.02 0 меньше a больше π

Answer 1

$0$ т.е. угол α/2 лежит в первой четверти и в этой четверти косинус положителен.

По формуле косинуса двойного угла, имеем $\cos \alpha=2\cos^2\dfrac{\alpha}{2}-1$

Тогда $2\cos^2\dfrac{\alpha}{2}-1=-0.02~~~\Leftrightarrow~~~ \cos^2\dfrac{\alpha}{2}=0.49$ откуда получаем $\cos\dfrac{\alpha}{2}=0.7$

Ответ: 0,7.

Answer 2

To find cos(a/2) given that cos(a) = -0.02 and a is between π and 0, we can use the half-angle identity for cosine.

The half-angle identity for cosine states that cos(a/2) = ±√[(1 + cos(a))/2].

Since a is between π and 0, it means that a is in the second quadrant where cosine is negative. So, cos(a) = -0.02 implies that cos(a/2) = -√[(1 + cos(a))/2].

Now, let's calculate cos(a/2) using the given value of cos(a):

cos(a/2) = -√[(1 + cos(a))/2] = -√[(1 + (-0.02))/2] = -√[(1 - 0.02)/2] = -√[0.98/2] = -√0.49 = -0.7

Therefore, cos(a/2) ≈ -0.7.