SOLUTION: If csc theta = -5/4 and 180degrees < theta < 270degree, find tan theta a. -4/3 b. 3/4 c. 4/3 d. -4/5

Algebra ->  Trigonometry-basics -> SOLUTION: If csc theta = -5/4 and 180degrees < theta < 270degree, find tan theta a. -4/3 b. 3/4 c. 4/3 d. -4/5      Log On


   

Question 339074: If csc theta = -5/4 and 180degrees < theta < 270degree, find tan theta
a. -4/3
b. 3/4
c. 4/3
d. -4/5
Answer by nyc_function(2741) About Me  (Show Source):
You can put this solution on YOUR website!
cosecant = hypotenuse/opposite
180 < theta < 270 tells me that we are in quadrant 3.
We form a right triangle in quadrant 3. The hypotenuse = -5 and the leg opposite the hypotenuse = 4. We are looking for the adjacent side of the right triangle.
Let A = adjacent side
A^2 + 4^2 = (-5)^2
A^2 + 16 = 25
A^2 = 25 - 16
A^2 = 9
sqrt[A^2] = sqrt[9]
A = 3
tangent = opposite side/adjacent
In quadrant 3, tangent is positive.
Answer: tan(theta) = 4/3...CHOICE (C).