Question

Знайти значення виразу cos 420°

Answer 1

Ответ:

1/2

Пошаговое объяснение:

cos 420 = cos 360 + cos 60 = cos 60 = 1/2

Answer 2

To find the value of the expression cos(420°), you first need to understand that trigonometric functions operate on angles measured in degrees or radians. In this case, we have an angle of 420 degrees.

However, the cosine function has a periodicity of 360 degrees (or 2π radians). This means that the value of cos(θ) is the same as cos(θ ± 360°) for any integer value of ± n.

So, cos(420°) is equivalent to cos(420° - 360°) because subtracting 360° brings us within one full cycle of the cosine function.

cos(420° - 360°) = cos(60°)

Now, cos(60°) is a well-known value. In a unit circle, the cosine of 60 degrees is equal to 1/2.

Therefore, cos(420°) = cos(60°) = 1/2.