Question

Знайти значення: sin240⁰ ; cos240⁰ ; sin1470⁰

Answer 1

Ответ:

- корень из 3 / 2

- 1/2

1/2

Пошаговое объяснение:

Answer 2

To find the values of trigonometric functions for the given angles, we need to use the unit circle.

In the unit circle, the angle is measured counterclockwise from the positive x-axis, and the coordinates (x, y) of the point where the angle intersects the circle give us the values of sine and cosine functions.

1. sin(240°):

To find sin(240°), we first need to find the point on the unit circle corresponding to this angle. Since 240° is between 180° and 270°, it lies in the third quadrant.

Using the symmetries of the unit circle, we can find that sin(240°) is equal to the negative value of sin(60°), as both angles have the same y-coordinate.

sin(60°) = √3/2 sin(240°) = -sin(60°) = -√3/2

2. cos(240°):

Again, for cos(240°), we look for the x-coordinate of the point corresponding to the angle 240° on the unit circle.

cos(240°) is equal to cos(60°) since both angles have the same x-coordinate.

cos(60°) = 1/2 cos(240°) = cos(60°) = 1/2

3. sin(1470°):

To find sin(1470°), we need to bring the angle within one full revolution (360°) since trigonometric functions are periodic.

1470° can be written as 4 * 360° + 90°. So, sin(1470°) is the same as sin(90°) since the sine function repeats every 360°.

sin(90°) = 1 sin(1470°) = sin(90°) = 1

In summary: sin(240°) = -√3/2 cos(240°) = 1/2 sin(1470°) = 1