katrinaaap
cos theta= - square root 2 divided by 2
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Mertsj
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\[\cos \theta= -\frac{\sqrt{2}}{2}\]
katrinaaap
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yeah I need to solve the equation (0<theta<2pi)
Mertsj
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We see that the cosine is negative. In what quadrants is the cosine negative?
katrinaaap
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2 and 3
Mertsj
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And on your unit circle, what angle has sqrt2/2 for its cosine?
katrinaaap
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-45
Mertsj
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45 does have that cosine ut we said we would be in quadrants II and III where the cosine is negative. Also you said your answer had to be between 0 and 2 pi so I think you should give the answer in radians.
Mertsj
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How many radians is 45 degrees?
katrinaaap
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45 degrees is pi/4
Mertsj
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So...in quadrants II and III:
Mertsj
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|dw:1368665856951:dw|
Mertsj
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What is the angle meassured from the positive x axis?
katrinaaap
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135
Mertsj
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radians, my dear.
katrinaaap
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3pi/4
Mertsj
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Yes. And now for the third quadrant answer:
katrinaaap
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5pi/4
Mertsj
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|dw:1368666064142:dw|
Mertsj
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Very good. And now you have your two answers. The angles between 0 and 2 pi that have a cosine of -sqrt2/2 are 3pi/4 and 5pi/4
katrinaaap
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perfect