Question 921352: Suppose sec t = 2 and csc t > 0. Find each of the following:
cos t =
cos (−t) =
cos (π + t) =
sin (−t) =
tan (t + π) =
I think I have this right since sec = 2 it's therefore 2/1 and that's hyp/opp so I use the Pythagorean theorem to find A
A^2 = 2^2 + 1^2
A = √(5)
So I have the opposite, adjacent and hypotenuse. I just don't understand what it's asking with -t? π+t? and t+π
please someone explain this
Thanks!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Suppose sec t = 2 and csc t > 0. Find each of the following:
------
Note: Since sec and csc are both positive, t is in QI where x and y are pos.
---------------------
cos t = 1/sec(t) = 1/2
-------------------------------
cos (−t) = 1/2 because cos(t) = cos(-t)
---------------------------------------
cos (π + t) = -1/2 because adding pi to the angle throws it into QIII
-----------------------
sin (−t) =
Since sec = 2 = r/y, x = sqrt[2^2-1^2] = sqrt(3)
So, sin(t) = sqrt(3)/2
Therefore sin(t) = -sqrt(3)/2 because the negative puts the angle into QIV
-----------------------------
tan (t + π) =
tan = sin/cos = (sqrt(3)/2)(1/2) = sqrt(3)
So, tan(t+pi) = sqrt(3) since adding pi puts the angle in QIII where sin
and cos are both negative.
============
Cheers,
Stan H.
================
|
|
|
