SOLUTION: If sin x=4/5 and pi/4 < x <pi/2 , Find sin(4x).

Algebra.Com
Question 639483: If sin x=4/5 and pi/4 < x Find sin(4x).
Answer by AnlytcPhil(1810)   (Show Source): You can put this solution on YOUR website!
sin x=4/5 and pi/4 < x < pi/2 ,
Find sin(4x)
Use the identity sin(2@) = 2sin(@)·cos(@) where @ = 2x

sin(4x) = sin[2(2x)] 

sin(4x) = 2sin(2x)·cos(2x)

Use that identity again with @=x to replace sin(2x).  Use
the identity cos(2@) = cosē(@)-sinē(@) to replace cos(2x)

sin(4x) = 2[2sin(x)·cos(x)][cosē(x)-sinē(x)]

sin(4x) = 4sin(x)·cos(x)[cosē(x)-sinē(x)] 

We have sin(x) =  but we don't have cos(x).  We use the identity
sinē(@)+cosē(@)=1 by solving it for cos(@)
        cosē(@)=1-sinē(@)
        cosē(x)=1-()ē = 1- =  = 
         cos(x)=
         cos(x)=
Sinve we are given that  < x < , we know that
the cosine is positive, therefore
         cos(x)=

sin(4x) = 4sin(x)·cos(x)[cosē(x)-sinē(x)]
sin(4x) = 4()·[-]
sin(4x) = [-]
sin(4x) = []
sin(4x) = 

Edwin
RELATED QUESTIONS

if cos x= -1/4 and pi/2 < x < pi, find the value of... (answered by Tutorteddy.Com)
Find the exact value if 0 < x < pi/2 and 0 < y < pi/2 ; sin(x+y) if sin(x) = 3/5 and... (answered by fractalier)
find range ?... (answered by mouk)
find sin(x+y) if tan(x)=4/3 and cos(y)=5/6, if 0 (answered by Alan3354)
sin(pi/2)-x (answered by stanbon)
sin(x+pi/2) (answered by Alan3354)
sin pi/5 = sin... (answered by Alan3354)
Given that cos x = 3/5 and sin x is positive. What is sin (x -pi), cos (x- pi), sin... (answered by rothauserc)
((cos(pi/4)+sin((pi/6))^2 (answered by greenestamps)