sin 45°
The sine of 45 degrees (sin 45°) is equal to √2/2
The sine of 45 degrees (sin 45°) is equal to √2/2.
To understand how to calculate this, we need to understand the unit circle and the concept of trigonometric functions.
The unit circle is a circle with a radius of 1 unit centered at the origin of a coordinate plane. It is used to define the values of trigonometric functions for different angles. The angles are measured in radians or degrees.
In trigonometry, the sine function (sin) represents the ratio of the length of the side opposite to an angle in a right triangle to the length of the hypotenuse.
For a right triangle with a 45 degree angle, if we draw that triangle in the unit circle, we will have a right isosceles triangle (a triangle with two equal sides and a right angle). In this triangle, the lengths of the two equal sides are both equal to 1 unit because it lies on the unit circle.
By applying the Pythagorean theorem, we can find the length of the hypotenuse. We have:
(1 unit)^2 + (1 unit)^2 = (hypotenuse)^2
1 + 1 = hypotenuse^2
2 = hypotenuse^2
√2 = hypotenuse
Therefore, the hypotenuse is √2 units. And since the sine of a 45-degree angle is the ratio of the side opposite to the hypotenuse, the sine of 45 degrees is (√2)/2.
So, sin 45° = √2/2.
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