SOLUTION: Find the quadrant (1, 2, 3, or 4) containing the points on the unit circle satisfying the given conditions. csc(t) > 0 tan(t) > 0

Algebra.Com
Question 616202: Find the quadrant (1, 2, 3, or 4) containing the points on the unit circle satisfying the given conditions.
csc(t) > 0
tan(t) > 0
Answer by fcabanski(1391)   (Show Source): You can put this solution on YOUR website!
CAST is the key to this. Starting in the 4th quadrant and moving counter clock wise, write CAST.


IV quadrant - only COS (and its reciprocal SEC) are positive.

I quadrant - All trig functions are positive.

II quadrant - SIN (and CSC) are positive.

III quadrant - TAN (and COT) are positive.


- Condition 1 indicates this is in quadrant I or II.

- Condition 2 (TAN must be positive) eliminates quadrant II (TAN is negative in quadrant II), so it must be quadrant I.


Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.)

RELATED QUESTIONS

Find the quadrant containing the point P on the unit circle U for the given conditions. (answered by Edwin McCravy)
Find the quadrant containing the point P on the unit circle U for the given conditions. (answered by Edwin McCravy)
Suppose cos t = -0.4 and csc t < 0 . Find each of the following sin t = tan t = csc (answered by ewatrrr)
Suppose cos t = -0.4 and csc t < 0 . Find each of the following sin t = tan t = (answered by lwsshak3)
If cos(t) = -2/3, and t is in quadrant III, find the exact values of sin(t), sec(t),... (answered by MathLover1,math_tutor2020)
Hi, I have 2 questions, Im so coonfused. 1) Let P be the point on the unit circle (answered by edjones)
A real number t is given. On a unit circle, draw the angle in standard position and arc... (answered by ikleyn)
Find all t in the interval [0, 2π] satisfying tan t - 3cot t =... (answered by Fombitz)
Find all values of t in the interval [0, 2π] satisfying the given equation. (Enter... (answered by jim_thompson5910)