SOLUTION: 1) Express tan t in terms of sin t, if the terminal point determined by t is in Quadrant III. 2) If cos t = −8/17 and if the terminal point determined by t is in Quadran

Algebra ->  Trigonometry-basics -> SOLUTION: 1) Express tan t in terms of sin t, if the terminal point determined by t is in Quadrant III. 2) If cos t = −8/17 and if the terminal point determined by t is in Quadran      Log On


   

Question 1028424: 1) Express tan t in terms of sin t, if the terminal point determined by t is in Quadrant III.

2) If cos t = −8/17 and if the terminal point determined by t is in Quadrant III,find tan t cot t + csc t.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
cos%28t%29=-8%2F17
sin%5E2%28t%29%2Bcos%5E2%28t%29=1
sin%5E2%28t%29%2B%28-8%2F17%29%5E2=1
sin%5E2%28t%29=1-64%2F289
sin%5E2%28t%29=225%2F289
sin%28t%29=0+%2B-+15%2F17
Since it's QIII,
sin%28t%29%3C0
sin%28t%29=-15%2F17
So then,
tan%28t%29=sin%28t%29%2Fcos%28t%29
tan%28t%29=%28-15%2F17%29%2F%28-8%2F17%29
tan%28t%29=15%2F8
.
.
.
tan%28t%29cot%28t%29%2Bcsc%28t%29=1%2B1%2Fsin%28t%29
tan%28t%29cot%28t%29%2Bcsc%28t%29=1%2B1%2F%28-15%2F17%29
tan%28t%29cot%28t%29%2Bcsc%28t%29=1-17%2F15
tan%28t%29cot%28t%29%2Bcsc%28t%29=15%2F15-17%2F15
tan%28t%29cot%28t%29%2Bcsc%28t%29=-2%2F15