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