SOLUTION: Find the exact values of sin(2u), and cos(2u), and tan(2u) using the double angle formulas. cot(u)=-5, 3pi/2 < u < 2pi

Algebra.Com
Question 1026041: Find the exact values of sin(2u), and cos(2u), and tan(2u) using the double angle formulas. cot(u)=-5, 3pi/2 < u < 2pi
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
 tells us that angle u is in
the fourth quadrant. 

Since  and we are given that
, we consider the  as ,
the we can make the numerator be the adjacent side of +5 and 
the denominator be -1.   

So we draw a right triangle in the fourth quadrant whose adjacent
side is +5 and whose opposite side is -1.  [We knew to consider
the -5 as  and not  because
+5 goes to the right and -1 goes down.] 

The angle u is represented by the red arc drawn counterclockwise
from the right side of the x-axis to the terminal side which is
the hypotenuse of the right triangle.

The hypotenuse is calculated from the Pythagorean theorem:




 <-- the hypotenuse is always positive!






Now we use some double angle identities:







We could use the formula for tan(2u), but it's easier
to use 



Edwin

RELATED QUESTIONS

Find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas. (answered by nyc_function)
find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas.... (answered by Solver92311)
Find the exact values of sin 2u,cos 2u, and tan 2u using the double-angle formulas. tan... (answered by Alan3354)
Find the exact values of sin 2u, cos 2u, and tan 2u using the double-angle... (answered by lwsshak3)
Find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas. (answered by Boreal,MathTherapy,Alan3354)
Find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas.... (answered by lwsshak3)
Find the exact values of sin 2u , Cos 2u, and tan 2u using double angle formulas. 1.... (answered by stanbon)
Find the exact values of sin 2u, cos 2u, and tan 2u using the double-angle formulas.cos u (answered by Alan3354)
Find the exact values of sin(2u),cos(2u),tan(2u)using the half-angle formulas. sin u =... (answered by greenestamps,ikleyn)