<p>Which of the following is the set of all read values of x such that 0 =< x =< 2pi and cos x = -1/2</p>
<p>A. {pi/6, 5pi/6}
B. {pi/3, 5pi/6}
C. {pi/2, 3pi/2}
D. {2pi/3, 4pi/3}
E. {2pi/3, 5pi/3}</p>
<p>The answer was D</p>
<p>But did the question mean for which set can the cos x = -1/2?</p>
<p>okay i will try to explain this the best i can</p>
<p>0 =< x =< 2pi
this means that the value is within the 4 quadrants or 360 degrees (2pi in radians)</p>
<p>cos x = -1/2
cos is negative only in the 2nd and 3rd quadrant
but with -1/2 it has to be in the 2nd (left one up two)
this creates a 30 60 90 triangle with sides of 1, 2, rad3, and an angle x of 60 degrees or 2pi/3
4pi/3 also creates the same angle and thus value in the 3rd quadrant</p>
<p>hope this helps, i know i didnt explain it very well haha</p>
<p>"But did the question mean for which set can the cos x = -1/2? "</p>
<p>Yes. The first part of the question (0 =< x =< 2pi) just meant that you had to restrict your answer for 0 radians to 2pi radians… or 0 degrees to 360 degrees. So it was really just find the values for which cosine equals -1/2 that fall between 0 radians and 2 pi radians. </p>
<p>All you have to do is set your calculator to radians, type in cosine inverse of -1/2 and you’ll get about 2.094 which is equivalent to 2pi/3. 4pi/3 also satisfies the problem. It equals exactly double 2.094… but with respect to the 3rd quadrant its cosine equals -1/2 so it works.</p>
<p>I hope this helps a little bit. The first answer may have said it better, but I thought I’d give you my input just in case. :)</p>