Pregunta
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\( \sin \left( \frac{\pi}{3} \right) = \frac{\sqrt{3}}{2} \)
Solución
Calculate or simplify the expression \( \sin(\frac{\pi}{3}) \).
Calculate the value by following steps:
- step0: Calculate:
\(\sin\left(\frac{\pi }{3}\right)\)
- step1: Calculate the trigonometric value:
\(\frac{\sqrt{3}}{2}\)
The value of \( \sin \left( \frac{\pi}{3} \right) \) is \( \frac{\sqrt{3}}{2} \).
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Simplifique esta solución Bonus Knowledge
The sine of \( \frac{\pi}{3} \) is a classic trigonometric value that many math enthusiasts enjoy. It equals \( \frac{\sqrt{3}}{2} \), which is derived from the special properties of a 30-60-90 triangle. In this triangle, the side opposite the 60-degree angle (or \( \frac{\pi}{3} \)) has a length of \( \sqrt{3} \), while the hypotenuse is 2. To remember this value, think of a unit circle where the coordinates at \( \frac{\pi}{3} \) are \( \left( \frac{1}{2}, \frac{\sqrt{3}}{2} \right) \). The y-coordinate represents the sine value, reinforcing the idea that the sine function relates to the vertical position on the circle. It’s a visual way to keep those tricky angles straight!
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