What is the value of sin 90 degrees?

The value of sine for an angle is defined based on the ratio of the length of the opposite side to the hypotenuse in a right triangle. However, for specific angles such as 90 degrees, it’s more common to refer to the unit circle definition of sine.

In the unit circle, a circle with a radius of 1, the point corresponding to 90 degrees (or π/2 radians) lies at the coordinates (0, 1). The sine of an angle is represented by the y-coordinate of this point. Therefore, for an angle of 90 degrees, since the y-coordinate is 1, the value of sin 90 degrees is 1.

Understanding this concept is fundamental, as it is a part of the foundational knowledge of trigonometric functions and their values at key angles, which are frequently used in various contexts within mathematics.