Question

Почему cos(pi/6)=корень3/2 почему объясните а то не понимаю.

Answer 1

Ответ:

Объяснение:

Пи/6 = 180/6 = 30°

cos 0° = 1

cos 30° = 0.86 = √3/2

Это значит, что если гипотенуза в прямоугольном треугольнике равна √3, а прилежащий к углу катет 2, то угол будет равен 30°

Answer 2

Explanation of cos(pi/6) = sqrt(3)/2

To understand why cos(pi/6) is equal to sqrt(3)/2, we need to look at the unit circle and the definition of cosine.

The unit circle is a circle with a radius of 1 centered at the origin of a coordinate plane. It is commonly used in trigonometry to define the values of trigonometric functions.

The cosine of an angle is defined as the x-coordinate of the point where the terminal side of the angle intersects the unit circle.

In the case of pi/6 (which is equivalent to 30 degrees), we can draw a right triangle within the unit circle. The angle pi/6 is formed by the x-axis and the terminal side of the angle.

The adjacent side of the triangle (the side adjacent to the angle) has a length of 1/2, and the hypotenuse (the radius of the unit circle) has a length of 1.

Using the Pythagorean theorem, we can find the length of the opposite side of the triangle:

opposite side = sqrt(hypotenuse^2 - adjacent side^2) = sqrt(1 - (1/2)^2) = sqrt(1 - 1/4) = sqrt(3/4) = sqrt(3)/2

Therefore, the cosine of pi/6 is equal to the x-coordinate of the point where the terminal side of the angle intersects the unit circle, which is equal to the adjacent side of the triangle:

cos(pi/6) = adjacent side / hypotenuse = (1/2) / 1 = 1/2

So, cos(pi/6) = 1/2.

To summarize: - The cosine of an angle is defined as the x-coordinate of the point where the terminal side of the angle intersects the unit circle. - For pi/6 (30 degrees), the adjacent side of the right triangle formed within the unit circle has a length of 1/2. - The hypotenuse of the triangle (the radius of the unit circle) has a length of 1. - Using the Pythagorean theorem, we can find that the opposite side of the triangle has a length of sqrt(3)/2. - Therefore, the cosine of pi/6 is equal to the adjacent side divided by the hypotenuse, which simplifies to 1/2.

I hope this explanation helps! Let me know if you have any further questions.