Asked by A

State the quadrant in which theta lies.

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

How can I determine this? Please explain.
Answered by Steve
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?
Answered by A
The answer would be quadrant 1, correct?
Answered by Steve
just so.
Answered by A
What about sec(theta) > 0 and cot(theta) < 0?
Would that be in quadrant 3?
Answered by A
Actually, I don't think it would. How can this one be determined?
Answered by A
It would be quadrant 4, correct?
Answered by Steve
yes
Answered by Bosnian
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
Answered by MathMate
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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