Answer:
-0.899
Explanation:
In the 4th quadrant, the sine is negative and the cosine is positive. The sine is ...
sin(-arccos(0.437)) ≈ -0.899
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You can also use the trig identity ...
sin(x) = -√(1 -cos(x)²) = -√(1 -.190969) = -√.809031 ≈ -0.89946150557
The sine is about -0.899.