ACT Question: If the value, to the nearest thousandth, of cos theta is -0.385, which of the following could be true about theta? a.) theta is greater than or equal to 0 and less than pi/6 b.) theta is greater than or equal to pi/6 and less than pi/3 c.) theta is greater than or equal to pi/3 and less than pi/2 d.) theta is greater than or equal to pi/2 and less than 2pi/3 e.) theta is greater than or equal to 2pi/3 and less than or equal to pi

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ACT Question: If the value, to the nearest thousandth, of cos theta is -0.385, which of the following could be true about theta? a.) theta is greater than or equal to 0 and less than pi/6 b.) theta is greater than or equal to pi/6 and less than pi/3 c.) theta is greater than or equal to pi/3 and less than pi/2 d.) theta is greater than or equal to pi/2 and less than 2pi/3 e.) theta is greater than or equal to 2pi/3 and less than or equal to pi

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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If the cosine of an angle is negative, then the angle is in either the second or third quadrant.
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Please explain it cause I know the answer from the back of the act book but I just dont get it
Im not helping. @SithsAndGiggles is already helping you why not try to understand them rather than bring attention to the post.
In terms of \(x,y,z\), you have \(\cos\theta=\dfrac{x}{z}\) (where \(\theta\) is the angle I mistakenly left out). \(z\) is always taken to be a positive number, so if the trig ratio is negative, either \(x\) or \(y\) must be negative.
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