SOLUTION: (1). Find all solutions for x (exact values in radians): {{{ 2sin(3x)cos(x) -sqrt(3) sin(3x)=0 }}} (2.) Let {{{ cos(u)=-(2/5)) }}} and {{{ pi/2<u<pi }}} Find each of the fol

Algebra ->  Trigonometry-basics -> SOLUTION: (1). Find all solutions for x (exact values in radians): {{{ 2sin(3x)cos(x) -sqrt(3) sin(3x)=0 }}} (2.) Let {{{ cos(u)=-(2/5)) }}} and {{{ pi/2<u<pi }}} Find each of the fol      Log On


   

Question 933502: (1). Find all solutions for x (exact values in radians): +2sin%283x%29cos%28x%29+-sqrt%283%29+sin%283x%29=0+


(2.) Let +cos%28u%29=-%282%2F5%29%29+ and +pi%2F2%3Cu%3Cpi+ Find each of the following
i. +cos%28u%2B11pi%2F6%29+
ii. +tan%28u-7pi%2F2%29+
THANK YOU
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
(1). Find all solutions for x (exact values in radians): +2sin%283x%29cos%28x%29+-sqrt%283%29+sin%283x%29=0+
2sin(3x)cosx-√3sin(3x)=0
sin(3x)(2cosx-√3)=0
cos(3x)=0
3x=0
3x=π/2+2πn, 2π/3+2πn, n=any integer
or
2cosx-√3=0
cosx=√3/2
x=π/6+2πn,11π/6+2πn, n=anyinteger
..
(2.) Let +cos%28u%29=-%282%2F5%29%29+ and +pi%2F2%3Cu%3Cpi+ Find each of the following:
sinu=√21/5
tanu=-√21/2
i. cos(u+11π/6)=cosu*(cos(11π/6)-sinu*sin(11π/6)
=(-2/5*+√(3)/2)-(√(21)/5*-(1/2))=-2√(3)/10+√(21))/10=(-2√(3)+√(21)/10
cos(u+11π/6)=(-2√(3)+√(21))/10
..
ii. +tan%28u-7pi%2F2%29+=(tanu-tan(7π/2))/(1+tanu*tan(7π/2))
no solution: tan(7π/2) is undefined