Understanding the Double-Angle Formula for Sine and Its Application in Trigonometry

sin 2x

The expression sin 2x represents the sine of twice the angle x

The expression sin 2x represents the sine of twice the angle x. In other words, it is the sine of the angle obtained by doubling the size of x.

To understand the value of sin 2x, we can use a trigonometric identity called the double-angle formula for sine. This formula states that sin 2x = 2sin x cos x.

Let’s break down the formula further to understand it better. The right-hand side of the equation consists of two parts: 2sin x and cos x. The 2sin x term represents twice the sine of x. The cos x term represents the cosine of x.

So, sin 2x is equal to the product of twice the sine of x and the cosine of x.

It is important to note that this formula provides a relationship between sin 2x and sin x and cos x. It allows us to express sin 2x in terms of sin x and cos x.

If you are given values for sin x and cos x, you can use the double-angle formula to find the value of sin 2x. Similarly, if you know the value of sin 2x, you can use the formula to find the values of sin x and cos x.

For example, if you are given that sin x = 1/2 and cos x = √3/2, you can substitute these values into the formula sin 2x = 2sin x cos x to find sin 2x. Here’s how:

sin 2x = 2sin x cos x
sin 2x = 2(1/2) (√3/2)
sin 2x = (√3/2)

So, if sin x = 1/2 and cos x = √3/2, then sin 2x = (√3/2).

Remember, the double-angle formula for sine is a useful tool for relating sin 2x to sin x and cos x, allowing you to simplify expressions or find unknown values in trigonometric problems.

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