Trigonometry

State the quadrant in which theta lies.

sin(theta) > 0 and cos(theta) > 0

How can I determine this? Please explain.

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  1. just recall the definition of the trig functions, in terms of a standard triangle.

    sin = y/r
    cos = x/r
    tan = y/x

    since r is always positive, you just need to ask yourself

    where are x and y both positive?

    do you feel lucky? . . . well, do ya?

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  2. The answer would be quadrant 1, correct?

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  3. just so.

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  4. What about sec(theta) > 0 and cot(theta) < 0?
    Would that be in quadrant 3?

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  5. Actually, I don't think it would. How can this one be determined?

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  6. It would be quadrant 4, correct?

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  7. yes

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  8. sec θ > 0

    cot θ < 0

    sec θ > 0

    1 / cos θ > 0

    If 1 / cos θ > 0 then also cos θ > 0

    cot θ < 0

    cos θ / sin θ < 0

    If cos > 0 cot θ = cos θ / sin θ can be < 0 only if sin θ < 0

    You must find quadrat where:

    cos θ > 0 and sin θ < 0

    In Quadrant IV, cos θ > 0, sin θ < 0

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  9. I prefer Steve's and Bosnian's method:
    if cos>0, right-hand quadrants.
    if sin>0, upper-quadrants
    if tan>0, 1st or 3rd quadrants.
    (sec same as cos, csc same as sin, cot same as tan)

    However, for checking, you can use the CAST method.

    S|A
    -+--
    T|C

    They correspond to the quadrants in which the trigonometric functions (cos, ALL, sin, tan) are positive.

    http://mathonweb.com/help_ebook/html/cast.htm

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