The expression sin x cos x can be rewritten in terms of sine by applying a well-known trigonometric identity. Specifically, we can utilize the double angle formula for sine, which states:
sin(2x) = 2 sin x cos x
From this identity, we can see that:
sin x cos x = (1/2) sin(2x)
This means that sin x cos x is equivalent to half of the sine of double the angle. Therefore, when you’re looking to express sin x cos x solely in terms of sine, the relationship can be summarized as:
sin x cos x = (1/2) sin(2x)Using this identity not only simplifies calculations involving sin x cos x, but it also shows the interconnectedness of the trigonometric functions.