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katrinaaap

  • 2 years ago

cos theta= - square root 2 divided by 2

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  1. Mertsj
    • 2 years ago
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    \[\cos \theta= -\frac{\sqrt{2}}{2}\]

  2. katrinaaap
    • 2 years ago
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    yeah I need to solve the equation (0<theta<2pi)

  3. Mertsj
    • 2 years ago
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    We see that the cosine is negative. In what quadrants is the cosine negative?

  4. katrinaaap
    • 2 years ago
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    2 and 3

  5. Mertsj
    • 2 years ago
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    And on your unit circle, what angle has sqrt2/2 for its cosine?

  6. katrinaaap
    • 2 years ago
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    -45

  7. Mertsj
    • 2 years ago
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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.

  8. Mertsj
    • 2 years ago
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    How many radians is 45 degrees?

  9. katrinaaap
    • 2 years ago
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    45 degrees is pi/4

  10. Mertsj
    • 2 years ago
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    So...in quadrants II and III:

  11. Mertsj
    • 2 years ago
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    |dw:1368665856951:dw|

  12. Mertsj
    • 2 years ago
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    What is the angle meassured from the positive x axis?

  13. katrinaaap
    • 2 years ago
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    135

  14. Mertsj
    • 2 years ago
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    radians, my dear.

  15. katrinaaap
    • 2 years ago
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    3pi/4

  16. Mertsj
    • 2 years ago
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    Yes. And now for the third quadrant answer:

  17. katrinaaap
    • 2 years ago
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    5pi/4

  18. Mertsj
    • 2 years ago
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    |dw:1368666064142:dw|

  19. Mertsj
    • 2 years ago
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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

  20. katrinaaap
    • 2 years ago
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    perfect

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