SOLUTION: Given tan(alpha)=2/sqrt(45) and alpha is in quadrant III, find the exact value of tan(alpha/2). Note: You are not allowed to use decimals in your answer. tan(alpha/2)=?

Algebra ->  Trigonometry-basics -> SOLUTION: Given tan(alpha)=2/sqrt(45) and alpha is in quadrant III, find the exact value of tan(alpha/2). Note: You are not allowed to use decimals in your answer. tan(alpha/2)=?      Log On


   

Question 860433: Given tan(alpha)=2/sqrt(45) and alpha is in quadrant III, find the exact value of tan(alpha/2).
Note: You are not allowed to use decimals in your answer.
tan(alpha/2)=?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Given tan(alpha)=2/sqrt(45) and alpha is in quadrant III, find the exact value of tan(alpha/2).
Note: You are not allowed to use decimals in your answer.
tan(alpha/2)= (1-cos(a))/sin(a)
cos(a) = x/r = ?
Since tan(a) = 2/sqrt(45) in QIII, y = -2 and x = -sqrt(45)
Then r = sqrt[45+4] = 7
---
cos(a) = x/r = -sqrt(45)/7
sin(a) = y/r = -2/7
------------------------------
Ans:: tan(a/2) = (1-(-sqrt(45)/7))/(-2/7)
---------
= -(1+sqrt(45))/(2)
=====================
Cheers,
Stan H.
=====================