This is a standard trigonometric value that should be memorised. The sine function represents the y-coordinate on a unit circle. At an angle of 90°, the point on the unit circle is at its highest point on the y-axis, which is (0, 1). Therefore, sin 90° = 1.
Full Answer
The value of sin 90° is a fundamental result in trigonometry. You can remember this by considering the graph of y = sin(x). The sine wave starts at 0 (sin 0° = 0), rises to its maximum value at 90°, returns to 0 at 180°, drops to its minimum value at 270°, and returns to 0 at 360°. The maximum value of the sine function is 1. Therefore, sin 90° = 1.
Common mistakes
✗ Confusing sin 90° with sin 0° (which is 0) or cos 90° (which is 0).
Expert