SOLUTION: find the exact value of TAN theta given that SIN of theta equals negative one half and theta is in quadrant three

Algebra ->  Trigonometry-basics -> SOLUTION: find the exact value of TAN theta given that SIN of theta equals negative one half and theta is in quadrant three      Log On


   

Question 1046129: find the exact value of TAN theta given that SIN of theta equals negative one half and theta is in quadrant three
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In the 3rd qudrant,
sin is negative ( -/+ )
cos is negative ( -/+ )
tan is positive ( -/- )
-------------------
+sin%28+theta+%29+=+-1%2F2+
and
+cos%28+theta+%29+=+-sqrt%28+1+-+sin%5E2%28+theta+%29+%29+
and
+tan%28+theta+%29+=+sin%28+theta+%29+%2F+cos%28+theta+%29+
+tan%28+theta+%29+=+-sin%28+theta+%29+%2F+%28-sqrt%28+1+-+sin%5E2%28+theta+%29+%29%29+
+tan%28+theta+%29+=+%28+-1%2F2%29+%2F+%28+-sqrt%28++1+-+1%2F4+%29+%29+
+tan%28+theta+%29+=+%28+1%2F2+%29+%2F+sqrt%28+3%2F4+%29+
+tan%28+theta+%29+=+%28+1%2F2+%29%2A%28+2%2Fsqrt%283%29+%29+
+tan%28+theta+%29+=+1+%2F+sqrt%283%29+
( note the tan in 3rd quadrant must be positive )