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?
State the quadrant in which theta lies.
sin(theta) > 0 and cos(theta) > 0
How can I determine this? Please explain.
9 answers
The answer would be quadrant 1, correct?
just so.
What about sec(theta) > 0 and cot(theta) < 0?
Would that be in quadrant 3?
Would that be in quadrant 3?
Actually, I don't think it would. How can this one be determined?
It would be quadrant 4, correct?
yes
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
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
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
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