Understanding the Sine Function and Evaluating sin(π/4) (45 degrees)

sin π/4 (45)

The sine function, denoted as sin(x), is a mathematical function that gives the ratio between the length of the side opposite to an angle in a right triangle and the length of the hypotenuse

The sine function, denoted as sin(x), is a mathematical function that gives the ratio between the length of the side opposite to an angle in a right triangle and the length of the hypotenuse. In other words, sin(x) = opposite/hypotenuse.

In your question, sin π/4 (45), π/4 represents the angle in radians. π (pi) is a mathematical constant approximately equal to 3.14159, and it is used to describe angles in the unit of radians. π/4 radians is equal to 45 degrees.

To evaluate sin(π/4), we can use the fact that sin(π/4) is equal to the ratio of the length of the side opposite to the angle (45 degrees) and the length of the hypotenuse in a right triangle.

Consider a right triangle where one of the angles is 45 degrees. Let’s assume that the hypotenuse has a length of 1 unit. In this case, the side opposite the 45-degree angle would also have a length of 1 unit. The adjacent side, which is the side adjacent to the angle but not the hypotenuse, would also be 1 unit.

Using the Pythagorean theorem, we can find the length of the adjacent side by subtracting the square of the length of the opposite side from the square of the hypotenuse. In this case, it would be (1^2 – 1^2) = 0. Therefore, the adjacent side has a length of 0 units.

Now we can use the sine function to find the value of sin(π/4). Since sin(π/4) = opposite/hypotenuse, we have sin(π/4) = 1/1 = 1.

So, sin π/4 (45) is equal to 1.

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