Understanding sin2x | double angle formula for sine and its application

sin2x

In mathematics, sin2x refers to the sine of double angle of x

In mathematics, sin2x refers to the sine of double angle of x. It can be expressed as sin(2x) or sometimes as sin^2(x). The notation sin^2(x) may cause confusion as it could be interpreted as the square of sine(x), however, it is important to note that sin2x is not equal to (sin(x))^2.

To understand sin2x, let’s first recall the double angle formula for sine:
sin(2x) = 2sin(x)cos(x)

This formula states that the sine of twice an angle (2x) is equal to twice the sine of the angle (x) multiplied by the cosine of the angle (x).

For example, if we consider x = π/4, we can find sin2x as follows:
sin(2(π/4)) = sin(π/2) = 1

Since sin(π/2) is equal to 1, we can conclude that sin2(π/4) = 1 for this particular value of x.

Similarly, by utilizing the double angle formula for sine, we can determine the value of sin2x for any angle x.

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