# 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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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

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 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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