Question 1033300: Use the given information to determine the exact trigonometric value.
If csc(theta)= -5/2 and 180 degrees < theta < 270 degrees; find the exact value of sin(2theta)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Use the given information to determine the exact trigonometric value.
If csc(theta)= -5/2 and 180 degrees < theta < 270 degrees; find the exact value of sin(2theta)
------
Note: sin = 1/csc, so sin(t) = y/r = -2/5
In QIII, y is negative.
So, y = -2 and r = 5
Then x = -sqrt[5^2-2^2] = -sqrt[21]
and cos(x) = -sqrt(21)/5
------------------------
Ans: sin(2t) = 2*sin(t)cos(5) = 2(-2/5)(-sqrt(21)/5) = -(4/25)sqrt(21)
============
Cheers,
stan H.
------------
|
|
|
