SOLUTION: Suppose cot t = −0.8 and t is in quadrant IV. Find each of the following sin (t + 4π) = tan (t + 11π) = please give detail on how these are solved. I've fi

Algebra ->  Trigonometry-basics -> SOLUTION: Suppose cot t = −0.8 and t is in quadrant IV. Find each of the following sin (t + 4π) = tan (t + 11π) = please give detail on how these are solved. I've fi      Log On


   

Question 922020: Suppose cot t = −0.8 and t is in quadrant IV. Find each of the following
sin (t + 4π) =
tan (t + 11π) =
please give detail on how these are solved. I've figured out that opposite = -5, adjacent = 4 and hypotenuse = √41 but I am stuck on solving these.
Thank you
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
You have a good start.

TIP:
Think of the period of the functions.
Sine has a period of 2pi , so it repeats after 2pi :
sin%28t%29=sin%28t%2B2pi%29=sin%28t%2B4pi%29=sin%28t%2B6pi%29= ...
Tangent has a period of pi , so tan%28t%2B11pi%29=tan%28t%29 .
In other words, all those extra pi's were there just to confuse you.

I was seeing it as , but that is a scaled down version of your bigger triangle,
and I like your big triangle better:
So sin%28t%29=-5%2Fsqrt%2841%29=-5sqrt%2841%29%2F41
Also, tan%28t%29=1%2Fcot%28t%29=1%2F0.8=1.25.
Then highlight%28sin%28t%2B4pi%29=-5sqrt%2841%29%2F41%29 and highlight%28tan%28t%2B11pi%29=1.25%29 .