Question

Знайти значення виразу cos 780°

Answer 1

cos780°=cos(720°+60°)=cos60°=0,5;

sin(13π/6)=sin(2π+π/6)=sin(π/6)=sin30°=0,5

это

Answer 2

To find the value of the expression cos 780°, we can use the unit circle and trigonometric identities.

First, we need to convert 780° into an equivalent angle within one full revolution (360°). We can do this by subtracting multiples of 360° until we get an angle between 0° and 360°.

780° - 2 * 360° = 60°

Now, we have 60° as an equivalent angle within one full revolution.

Next, we find the cosine of 60°. In the unit circle, cosine is the x-coordinate of the point corresponding to the angle.

For 60°, the point on the unit circle lies in the first quadrant, making an equilateral triangle with the center and two other points. The coordinates of that point are (cos 60°, sin 60°).

In an equilateral triangle, all angles are 60°, and the sides are equal. Since the radius of the unit circle is 1, the x-coordinate (cos 60°) is 1/2.

So, the value of cos 780° is:

cos 780° = cos 60° = 1/2