Explain why sin(90)=1

The length of the opposite side is the same as the length of the hypotenuse (they are the same side in this case), the ratio is:

sin(90 degrees) = 1 / 1 = 1

Thus, sin(90 degrees) equals 1.

In trigonometry, the sine function (abbreviated as sin) is defined based on the angles of a right-angled triangle.

Specifically, for a given angle θ in a right-angled triangle, the sine of θ is defined as the ratio of the length of the side opposite θ to the length of the hypotenuse (the longest side of the triangle, which is always opposite the right angle).

In a standard coordinate system, consider a right-angled triangle where one of the angles is 90 degrees (a right angle).

This angle is often denoted as π/2 radians in radians or 90 degrees in degrees.

In this triangle, the side opposite the angle θ (the side opposite the right angle) is the vertical side, and the hypotenuse is the longest side.

For a right-angled triangle with a 90-degree angle, the sine of θ is defined as:

sin(90 degrees) = length of opposite side / length of hypotenuse

Since the length of the opposite side is the same as the length of the hypotenuse (they are the same side in this case), the ratio is:

sin(90 degrees) = 1 / 1 = 1

Thus, sin(90 degrees) equals 1.

In radians, sin(π/2 radians) is also equal to 1 since it is the same angle as 90 degrees but measured in radians.

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