What is cos(x) sin(x)?
Understand the Problem
The question is asking for the product of the cosine and sine of an angle x, which is a basic concept in trigonometry. It might imply a need to simplify or use this expression in a mathematical context.
Answer
$$ P = \frac{1}{2} \sin(2x) $$
Answer for screen readers
$$ P = \frac{1}{2} \sin(2x) $$
Steps to Solve
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Identify the expression
We are looking for the product of cosine and sine of angle $x$, which can be represented as:
$$ P = \cos(x) \cdot \sin(x) $$ -
Use a trigonometric identity
There is a useful trigonometric identity that relates the product of sine and cosine to sine of double angle:
$$ P = \frac{1}{2} \sin(2x) $$
This means that the product can also be expressed in terms of the sine function of double the angle. -
Final expression
Thus, the expression for the product of cosine and sine can be simplified to:
$$ P = \frac{1}{2} \sin(2x) $$
$$ P = \frac{1}{2} \sin(2x) $$
More Information
The expression $P = \frac{1}{2} \sin(2x)$ shows that the product of sine and cosine can be connected to the sine of a double angle. This identity is useful in various applications in physics and engineering, particularly in wave functions.
Tips
One common mistake is forgetting to apply the double angle identity correctly, or trying to calculate the product without recognizing the simplification opportunities. To avoid this, always check for trigonometric identities that can simplify your work.
