Answer:
\(\boxed{\boxed{0.954}}\)
Step-by-step explanation:
We know that \(\sf \sin \theta = -0.299\).
Given that \(\sf \dfrac{3\pi}{2} < \theta < 2\pi\), we are in the forth quadrant where cosine is positive.
Using the identity \(\sf \sin^2 \theta + \cos^2 \theta = 1\), we can find \(\sf \cos \theta\):
\(\sf \cos^2 \theta = 1 - \sin^2 \theta\)
\(\sf \cos^2 \theta = 1 - (-0.299)^2\)
\(\sf \cos^2 \theta = 1 - 0.089401\)
\(\sf \cos^2 \theta \approx 0.910599\)
Taking the square root of both sides:
\(\sf \cos \theta \approx \sqrt{0.910599}\)
\(\sf \cos \theta \approx 0.9542531110769\)
So,
\(\sf \cos \theta \approx 0.954 \textsf{ (in nearest thousandth)}\)
So, \(\sf \cos \theta\) is approximately \(\sf 0.954\).
