What is the value of sin(90°)?

What is the value of sin(90°)?

• A. 0
• B. 0.5
• C. 1
• D. 1.5

Answer: (C)

The value of sin(90°) is 1 because, in trigonometric terms, the sine of an angle in a right triangle refers to the ratio of the length of the opposite side to the length of the hypotenuse. At 90 degrees, the angle corresponds to a point on the unit circle where the coordinates are (0, 1). This means that the vertical coordinate (which represents the sine value) is equal to 1, while the horizontal coordinate is 0. Therefore, sin(90°) is defined to be 1, reflecting the maximum value the sine function can obtain. Understanding this concept is critical in trigonometry because it sets the foundation for understanding the behavior of the sine function across different angles, particularly as it relates to the unit circle where all sine values range from -1 to 1.

The value of sin(90°) is 1 because, in trigonometric terms, the sine of an angle in a right triangle refers to the ratio of the length of the opposite side to the length of the hypotenuse. At 90 degrees, the angle corresponds to a point on the unit circle where the coordinates are (0, 1). This means that the vertical coordinate (which represents the sine value) is equal to 1, while the horizontal coordinate is 0. Therefore, sin(90°) is defined to be 1, reflecting the maximum value the sine function can obtain.

Understanding this concept is critical in trigonometry because it sets the foundation for understanding the behavior of the sine function across different angles, particularly as it relates to the unit circle where all sine values range from -1 to 1.