Understanding the Sine Function | Exploring the Value of sin(45°) in Trigonometry

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.

More Answers: