sin45
In trigonometry, the sine function (sin) represents a ratio between the length of the side opposite to an angle in a right triangle and the hypotenuse (the longest side) of the triangle
In trigonometry, the sine function (sin) represents a ratio between the length of the side opposite to an angle in a right triangle and the hypotenuse (the longest side) of the triangle. It is defined as:
sin(angle) = opposite / hypotenuse
In the case of sin(45°), we are looking for the sine of a 45-degree angle. To find this value, we can use the fact that in a 45-45-90 right triangle, the two legs are congruent, and the hypotenuse is √2 times the length of the legs.
Thus, if we assume that the legs have a length of 1, the hypotenuse will be √2. And since sin(angle) = opposite / hypotenuse, sin(45°) would be:
sin(45°) = 1 / √2
Now, it is common to rationalize the denominator (i.e., remove the square root from the denominator) to have a more simplified expression. To do this, we multiply the numerator and denominator by the square root of 2:
sin(45°) = (1 / √2) * (√2 / √2)
= √2 / 2
So the exact value of sin(45°) is √2 / 2, which is approximately equal to 0.707.
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