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kittiwitti1

  • one year ago

As θ increases from 0° to 90°, the value of cos θ tends toward which of the following? Answers available: 0 and 1. (Putting pos/neg infinity is wrong so I just need to decide which).

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  1. mathstudent55
    • one year ago
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    |dw:1441598341152:dw|

  2. mathstudent55
    • one year ago
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    The cosine of an angle is the x-coordinate of the point of intersection of the terminal side of the angle and the unit circle.

  3. mathstudent55
    • one year ago
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    |dw:1441598453980:dw|

  4. kittiwitti1
    • one year ago
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    Is the answer 0?

  5. mathstudent55
    • one year ago
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    When theta = 0 deg, cos(theta) = 1, since the x-coordinate of the point of intersection of the terminal side of of a zero-degree angle (in standard position) and the unit circle is 1.

  6. kittiwitti1
    • one year ago
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    I mean, the x-values are steadily decreasing so I assumed 0, but I am just making sure.

  7. mathstudent55
    • one year ago
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    Correct.

  8. kittiwitti1
    • one year ago
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    Thank you :)

  9. mathstudent55
    • one year ago
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    |dw:1441598614600:dw|

  10. mathstudent55
    • one year ago
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    As theta goes from 0 deg to 90 deg, the x-coordinate goes from 1 to 0.

  11. mathstudent55
    • one year ago
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    You're welcome.

  12. kittiwitti1
    • one year ago
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    @mathstudent55 could you help me with this one as well? cos θ = 1/2 and θ terminates in QIV. So far I have this: http://prntscr.com/8dhn18

  13. anonymous
    • one year ago
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    \[\sin(\theta)=\pm\sqrt{1-\frac{1}{4}}=\pm\sqrt{\frac{3}{4}}=\pm\frac{\sqrt{3}}{2}\] Since theta is in 4th quadrant, sin will be negative \[\sin(\theta)=-\frac{\sqrt{3}}{4}\] There is a reason why you are given in which quadrant theta belongs to, so you can apply proper signs!

  14. kittiwitti1
    • one year ago
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    Thanks @Nishant_Garg :]

  15. mathstudent55
    • one year ago
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    @Nishant_Garg \(\large \sin(\theta)=\pm\sqrt{1-\frac{1}{4}}=\pm\sqrt{\frac{3}{4}}=\pm\frac{\sqrt{3}}{2}\) \(\large \sin(\theta)=-\frac{\sqrt{3}}{\huge \color{red}{4}}\) ?

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