To solve the problem of finding [tex]\( E = \sin(\theta) \cos(\theta) \)[/tex] given [tex]\(\tan(\theta) = 0.333\)[/tex], we need to follow a series of steps.
1. Find [tex]\(\theta\)[/tex]:
We begin by identifying the angle [tex]\(\theta\)[/tex] such that [tex]\(\tan(\theta) = 0.333\)[/tex]. This implies we need to find [tex]\(\theta = \arctan(0.333)\)[/tex].
With this, we get:
[tex]\[
\theta = \arctan(0.333) \approx 0.3214505244026446 \text{ radians}
\][/tex]
2. Calculate [tex]\(\sin(\theta)\)[/tex]:
Next, we need the sine of the angle [tex]\(\theta\)[/tex]:
[tex]\[
\sin(\theta) = \sin(0.3214505244026446) \approx 0.31594311834379357
\][/tex]
3. Calculate [tex]\(\cos(\theta)\)[/tex]:
Similarly, we need the cosine of the angle [tex]\(\theta\)[/tex]:
[tex]\[
\cos(\theta) = \cos(0.3214505244026446) \approx 0.9487781331645453
\][/tex]
4. Calculate [tex]\(E = \sin(\theta) \cos(\theta)\)[/tex]:
Finally, we compute the product [tex]\(E\)[/tex]:
[tex]\[
E = \sin(\theta) \cos(\theta) = 0.31594311834379357 \times 0.9487781331645453 \approx 0.29975992200840945
\][/tex]
5. Determine the Correct Option:
Comparing the numerical result with the given options:
[tex]\[
0.29975992200840945 \approx \frac{3}{10} = 0.3
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{\frac{3}{10}}
\][/tex]
