SOLUTION: Suppose sin t = 4 7 and cos t < 0. Find each of the following (exact values): cos t = tan t = csc t = sec t = cot t = Please explain Thank you

Algebra ->  Trigonometry-basics -> SOLUTION: Suppose sin t = 4 7 and cos t < 0. Find each of the following (exact values): cos t = tan t = csc t = sec t = cot t = Please explain Thank you      Log On


   

Question 986631: Suppose sin t =
4
7
and cos t < 0. Find each of the following (exact values):

cos t =
tan t =
csc t =
sec t =
cot t =
Please explain
Thank you
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose sin t = (4/7)
and cos t < 0. Find each of the following (exact values):
-----
Those conditions imply that "t" is in the 2nd Quadrant
where y is positive and x is negative.
--------------
By defition, sin = y/r
Since sin = 4/7, y = 4 and r = 7
Solve for "x" (which is negative)
---
x = =sqrt[7^2-4^2] = -sqrt(49-16) = -sqrt(33)
----
cos t = x/r = -sqrt(33)/7
-------
tan t = y/x = -4/sqrt(33)
----------
csc t = r/y = 7/4
-----------
sec t = r/x = -7/sqrt(33)
-----------
cot t = x/y = -sqrt(33)/4
------------------
Cheers,
Stan H.
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