Express each of the following in terms of the cosine of another angle between 0 degrees and 180 degrees:

a) cos 20 degrees b) cos 85 degrees c) cos 32 degrees

d) cos 95 degrees e) cos 147 degrees f) cos 106 degrees

My answer:

a) - cos 160 degrees b) - cos 95 degrees c) -cos 148 degrees

d) -cos 85 degrees e) - cos 33 degrees f) - cos 74 degrees

Textbook answer:

a) cos 340 degrees b) cos 275 degrees c) cos 328 degrees

d) cos 265 degrees e) cos 213 degrees f) cos 254 degrees

My question: I do understand that the cosine of 20 degrees and 340 degrees are equal; but why are the answers greater than 180 degrees even though I was instructed to express my answer as the cosine of another angle between 0 degrees and 180 degrees.

clearly they mistyped the question. Your answers are all correct, and theirs are too, if the want answers between 180 and 360

thanks oobleck appreciate it

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When expressing each angle in terms of the cosine of another angle between 0 degrees and 180 degrees, the answer provided in the textbook is incorrect. You are correct in saying that the cosine of 20 degrees is equal to the cosine of 340 degrees.

The angles you provided as your answers in terms of cosine are actually correct. For example:

a) cos 20 degrees = -cos 160 degrees
b) cos 85 degrees = -cos 95 degrees
c) cos 32 degrees = -cos 148 degrees
d) cos 95 degrees = -cos 85 degrees
e) cos 147 degrees = -cos 33 degrees
f) cos 106 degrees = -cos 74 degrees

All of these angles fall between 0 degrees and 180 degrees, and they are expressed in terms of the cosine of another angle. The textbook answers provided (cos 340 degrees, cos 275 degrees, cos 328 degrees, etc.) are not between 0 degrees and 180 degrees and do not satisfy the given conditions.