sinifunktio

The sinifunktio, often referred to as the sine function in English, is a fundamental trigonometric function. It relates an angle of a right-angled triangle to the ratio of the length of the side opposite the angle to the length of the hypotenuse. Mathematically, for an angle $\theta$, $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$.

The graph of the sinifunktio, known as a sine wave, is a periodic curve that oscillates between values of -1 and 1. Its period is $2\pi$ radians or 360 degrees, meaning the function repeats its pattern every $2\pi$ interval. Key points on the graph include where the function equals 0 (at multiples of $\pi$), 1 (at $\frac{\pi}{2} + 2n\pi$), and -1 (at $\frac{3\pi}{2} + 2n\pi$, where $n$ is an integer).

The sinifunktio has wide-ranging applications in various fields. It is crucial in trigonometry, calculus, and physics, particularly in describing wave phenomena such as sound waves, light waves, and alternating currents. It also appears in engineering, signal processing, and celestial mechanics. The Taylor series expansion for the sinifunktio is $\sin(x) = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \dots$, which is useful for approximating its values.