Question

Cos120=cos(180-60)=-cos60 откуда взялись 180 и 60?

Answer 1

Объяснение:

Cos120 = -0,5

Cos180 = -1

Cos60 = 0,5

Это просто выражение 180-60=120, аналогично работающее и с косинусами.

Answer 2

The values 180 and 60 in the trigonometric expressions you mentioned are derived from the properties of the unit circle and the periodicity of trigonometric functions.

Let's break it down step by step:

1. Unit Circle: The unit circle is a circle with a radius of 1 unit centered at the origin (0, 0) in the Cartesian coordinate system.

2. Cosine Function: The cosine function is defined as the x-coordinate of a point on the unit circle corresponding to a specific angle θ.

3. 180 Degrees: On the unit circle, an angle of 180 degrees corresponds to the point (-1, 0), which means cos(180°) = -1. This is because the x-coordinate is -1 at that position.

4. 60 Degrees: On the unit circle, an angle of 60 degrees corresponds to the point (1/2, √3/2), which means cos(60°) = 1/2. This is because the x-coordinate is 1/2 at that position.

Now, let's look at the two trigonometric expressions you mentioned:

1. cos(120°): This angle lies in the second quadrant of the unit circle (between 90° and 180°). Since the cosine function is negative in the second quadrant, cos(120°) = -cos(180° - 120°) = -cos(60°).

2. cos(180° - 60°): This expression represents an angle that is the difference between 180° and 60°, which is 120°. As we saw earlier, cos(120°) is -cos(60°), so cos(180° - 60°) = -cos(60°).

Therefore, both expressions are equal to -cos(60°).