Is 1/2 sin 2x the same expression as sin x? Justify your answer.
sin(2x)=2*sin(x)*cos(x)
(1/2)sin(2x)=(1/2)*2*sin(x)*cos(x)=sin(x)*cos(x)
(1/2)sin(2x)=sin(x)*cos(x)
To determine whether 1/2 sin 2x is the same expression as sin x, we can simplify 1/2 sin 2x using trigonometric identities.
Using the double angle identity for sine, sin 2x can be expressed as 2sin x cos x.
Substituting this into the given expression, we have:
1/2(2sin x cos x) = sin x cos x.
Since sin x cos x is not equivalent to sin x, we can conclude that 1/2 sin 2x is not the same expression as sin x.
To determine if 1/2 sin 2x is the same expression as sin x, we need to compare their functions and simplify the given expression if possible.
Let's start by examining the given expression, 1/2 sin 2x.
The function sin x represents the sine of an angle x.
On the other hand, 1/2 sin 2x represents the product of two components: 1/2 and sin 2x.
To determine if these two expressions are equivalent, we can simplify 1/2 sin 2x and see if it matches the function sin x.
Using the double angle formula for sine, sin 2x can be expressed as 2sin x cos x.
Now we can substitute sin 2x with 2sin x cos x in the expression 1/2 sin 2x:
1/2 * 2sin x cos x
The coefficient 1/2 can be simplified by canceling out the factor of 2:
(1/2) * 2sin x cos x
= sin x cos x
Based on the above simplification, we can conclude that 1/2 sin 2x is not the same expression as sin x. The expression 1/2 sin 2x simplifies to sin x cos x, which has an additional factor of cos x compared to sin x.
Therefore, 1/2 sin 2x is not equivalent to sin x.