What is the exact value of sin 0°?

The exact value of sin 0° is 0.

In trigonometry, the sine function relates the angle of a right-angled triangle to the ratio of the length of the opposite side to the hypotenuse. When the angle is 0°, the opposite side length is 0 because the angle essentially flattens the triangle, making the opposite side coincide with the adjacent side. Since the hypotenuse is never zero, the ratio of 0 (opposite side) to any positive number (hypotenuse) is 0. Therefore, sin 0° = 0.

Visualising this on the unit circle, which is a circle with a radius of 1 centred at the origin of a coordinate plane, can also help. The sine of an angle in the unit circle is the y-coordinate of the point where the terminal side of the angle intersects the circle. At 0°, this point is (1, 0). The y-coordinate here is 0, confirming that sin 0° = 0.

Understanding this concept is fundamental in trigonometry and helps in solving more complex problems involving trigonometric functions. Remember, the sine function is periodic and continuous, meaning it repeats its values in a regular pattern and has no breaks. This property is useful when analysing wave patterns, oscillations, and other phenomena in both mathematics and physics.