SOLUTION: Find the values of the trigonometric functions of t from the given information. sec(t) = 3, terminal point of t is in Quadrant IV

Algebra ->  Trigonometry-basics -> SOLUTION: Find the values of the trigonometric functions of t from the given information. sec(t) = 3, terminal point of t is in Quadrant IV      Log On


   

Question 1197483: Find the values of the trigonometric functions of t from the given information.
sec(t) = 3, terminal point of t is in Quadrant IV
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
sec%28t%29+=+3, terminal point of t+is in Quadrant IV

if sec%28t%29+=+3, then cos%28+t%29+=1%2F3+ (using identity cos%28+t%29+=1%2F+sec%28t%29%29

using identity sin%5E2%28t%29%2B+cos%5E2%28t%29=1 calculate sin%28t%29

sin%28t%29=sqrt%281-cos%5E2%28t%29%29
sin%28t%29=sqrt%281-%281%2F3%29%5E2%29
sin%28t%29=sqrt%288%2F9%29
sin%28t%29=%282sqrt%282%29%29%2F3 or sin%28t%29=-%282sqrt%282%29%29%2F3

in Quadrant IV only cos%28+t%29%3E0
so, take negative value for sin
cos%28+t%29+=1%2F3
sin%28t%29=-%282sqrt%282%29%29%2F3

tan%28+t%29+=-%28%282sqrt%282%29%29%2F3%29%2F%281%2F3%29=-2sqrt%282%29

cot+%28t%29=%281%2F3%29%2F%28-%282sqrt%282%29%29%2F3%29=-1%2F2sqrt%282%29-> rationalize cot+%28t+%29=-sqrt%282%29%2F4

csc+%28t+%29=+1%2Fsin%28t%29=1%2F%28-%282sqrt%282%29%29%2F3%29=-3%2F%282sqrt%282%29%29-> rationalize csc+%28t+%29=-%283sqrt%282%29%29%2F4