What is the value of sin(90°)?

What is the value of sin(90°)?

• A. 0
• B. 0.5
• C. 1
• D. Undefined

Answer: (C)

The value of sin(90°) is 1 because, on the unit circle, the sine function represents the y-coordinate of a point on the circle corresponding to a given angle. At an angle of 90°, the point on the unit circle is located at (0, 1), where the y-coordinate is 1. This means the sine of 90 degrees is precisely equal to 1, reflecting the highest vertical point on the unit circle. Hence, the correct answer is C. This relationship is a fundamental aspect of trigonometry, as the sine function varies between -1 and 1 over its range of angles, and knowing standard values like sin(0°) = 0, sin(30°) = 0.5, and sin(90°) = 1 is crucial for solving many mathematical problems involving triangles, circles, and periodic functions.

The value of sin(90°) is 1 because, on the unit circle, the sine function represents the y-coordinate of a point on the circle corresponding to a given angle. At an angle of 90°, the point on the unit circle is located at (0, 1), where the y-coordinate is 1. This means the sine of 90 degrees is precisely equal to 1, reflecting the highest vertical point on the unit circle. Hence, the correct answer is C.

This relationship is a fundamental aspect of trigonometry, as the sine function varies between -1 and 1 over its range of angles, and knowing standard values like sin(0°) = 0, sin(30°) = 0.5, and sin(90°) = 1 is crucial for solving many mathematical problems involving triangles, circles, and periodic functions.