What is sin2x=0?

The equation sin(2x) = 0 is a trigonometric equation. To solve it, we need to find the values of x for which the sine of 2x is equal to zero.

• General Solution: The sine function is zero at integer multiples of π (pi). Therefore, we can write:

  2x = nπ, where n is an integer (..., -2, -1, 0, 1, 2, ...)

  Dividing both sides by 2, we get:

  x = (nπ)/2

• Specific Solutions: This means that the solutions for x occur at x = 0, π/2, π, 3π/2, 2π, and so on, as well as the negative counterparts. We can also express this as x = 0°, 90°, 180°, 270°, 360° and so on.

• Understanding the Double Angle: The 2x inside the sine function means that the period of the sine wave is compressed. A normal sine wave, <a href="https://www.wikiwhat.page/kavramlar/Sine%20Wave">sine wave</a>, completes one full cycle between 0 and 2π. However, sin(2x) completes two full cycles between 0 and 2π.

• Graphical Representation: The graph of y = sin(2x) intersects the x-axis (where y=0) at the values of x we found as solutions. This highlights the periodic nature and the double frequency. The <a href="https://www.wikiwhat.page/kavramlar/Trigonometric%20Functions">Trigonometric Functions</a> value is zero where the graph cuts the x-axis.

• Related Concepts: This type of problem involves understanding <a href="https://www.wikiwhat.page/kavramlar/Trigonometry">Trigonometry</a>, the unit circle, and the behavior of trigonometric functions. It can appear in calculus when dealing with integrals and derivatives of trigonometric expressions, as well as in physics when modeling oscillatory motion.