sin 2x
In mathematics, sin 2x refers to the sine function applied to an angle that is twice the angle x
In mathematics, sin 2x refers to the sine function applied to an angle that is twice the angle x. The sine function is a trigonometric function that relates the ratio of the length of the side opposite an acute angle in a right triangle to the length of the hypotenuse.
To understand sin 2x, let’s break it down further using a trigonometric identity called the double angle formula for the sine function. The double angle formula states:
sin 2x = 2sin x cos x
This formula expresses sin 2x in terms of sin x and cos x. It shows that sin 2x can be calculated by taking the sine of x, multiplying it by the cosine of x, and then doubling the result.
Using this formula, you can find the value of sin 2x for a specific angle x. Let’s say x is 30 degrees. We can substitute this value into the formula:
sin 2(30) = 2sin 30 cos 30
sin 2(30) = 2 * (1/2) * (√3/2)
sin 2(30) = √3/2
Therefore, sin 2(30) is equal to √3/2.
In summary, sin 2x represents the sine function applied to an angle that is twice the angle x. It can be calculated using the double angle formula for sine: sin 2x = 2sin x cos x.
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