sin 2x
In mathematics, the function sin(2x) refers to the sine of the angle 2x
In mathematics, the function sin(2x) refers to the sine of the angle 2x. The sine is a trigonometric function that relates the ratio of the length of the side opposite to an angle in a right triangle to the length of the hypotenuse.
When dealing with sin(2x), it means that we are taking the sine of the angle 2x. This can be thought of as if we have a right triangle and one of the angles is 2x.
To understand how sin(2x) behaves, we can use the double-angle identity of trigonometric functions. This identity states that sin(2x) can be written as 2*sin(x)*cos(x). Here, sin(x) refers to the sine of the angle x, and cos(x) refers to the cosine of the angle x.
So, if we are given sin(2x), we can find its value using this identity. We first find the sine of x and the cosine of x, then multiply them by 2, and finally multiply the two results together.
For example, let’s say we want to find the value of sin(2x) where x is 30 degrees. First, we find the sine of 30 degrees, which is 0.5, and the cosine of 30 degrees, which is (√3)/2. Then, using the double-angle identity, we multiply 0.5 and (√3)/2 each by 2 and multiply the results together:
sin(2x) = 2*sin(x)*cos(x)
sin(2*30) = 2*sin(30)*cos(30)
sin(60) = 2*(0.5)*((√3)/2)
sin(60) = (√3)/2
Therefore, sin(2x) when x is 30 degrees is (√3)/2.
The same process can be applied using radians instead of degrees. Remember to use the appropriate conversion factor between degrees and radians when necessary.
In summary, sin(2x) refers to the sine of the angle 2x, and its value can be found using the double-angle identity of trigonometric functions.
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