Question 841416: Given tan(theta)=-4/5 and cos(theta)>0, find the exact values of sin(theta) and sec(theta).
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Given tan(theta)=-4/5 and cos(theta)>0, find the exact values of sin(theta) and sec(theta).
----
Since tan is negative and cos is positive, theta is in QIV where
x is positive and y is negative.
------------------------------------
tan = y/x = -4/5 implies x = 5 and y = -4
----
Then r = sqrt[5^2+4^2] = sqrt(41)
----------------
Your Problem:
sin(t) = y/r = -4/sqrt(41)
----
sec(t) = r/x = sqrt(41)/5
-------------------------------
Cheers,
Stan H.
=======================
|
|
|
