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kozy

  • 3 years ago

Find all solutions in the interval [0, 2π). cos x = sin x

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  1. cwrw238
    • 3 years ago
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    divide both sides by cos x to give tan x = 1

  2. kozy
    • 3 years ago
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    okay got that

  3. cwrw238
    • 3 years ago
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    the tangent is positive in the first and 3rd quadrants

  4. kozy
    • 3 years ago
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    so that gives me pi/4, 7pi/4?

  5. cwrw238
    • 3 years ago
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    pi/4 is correct

  6. cwrw238
    • 3 years ago
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    |dw:1364766655163:dw|

  7. kozy
    • 3 years ago
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    I have two options with pi/4.. they are 7pi/4 or 5pi/4

  8. cwrw238
    • 3 years ago
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    5pi/4 is correct

  9. cwrw238
    • 3 years ago
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    pi/4 is in third quadrant

  10. RadEn
    • 3 years ago
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    alternative : cosx =sinx cosx = cos(90-x) cosx = cos(k*360 + 90-x) x = k*360 + 90-x 2x = k*360 + 90 x = k*180 + 45 for k=0, ---> x = 45 degrees for k=1, ---> x = 225 degrees convert all x to units pi radian, just divides by 180

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