Final answer:
The product of cosine values from 0° to 180° is zero because it includes cos(90°), which equals zero. Multiplying any number by zero results in zero, leading to the entire product being zero.
Step-by-step explanation:
When we take the cosine of any angle, we get the ratio of the adjacent side to the hypotenuse in a right-angled triangle. As cosine values for angles larger than 90° are negative, and since cos(90°) = 0, the product of cosines from 0° to 180° will always include cos(90°), hence resulting in a product of zero. This is because any real number multiplied by zero equals zero. Therefore, regardless of the values of cosines for other angles, the entire product is ultimately zero due to the presence of cos(90°). To summarize, cos(0°) cos(1°) cos(2°) … cos(180°) is nearly equal to zero because it contains the multiplication of cos(90°), which is zero. Any number multiplied by zero gives zero, which is why the entire product is zero, regardless of the values of the remaining cosine factors.