Question

Please help to solve this.
Find sin5x,if sinx+cosx=1,4

Answer 1

Hello,

Explanation:

we must first remember that:

`\boxed{sin(5x)=5sin(x)-20*sin^3(x)+16*sin^5(x)}\\\\`

Let say t=sin(x)

`sin(x)+cos(x)=1.4\\\\t+√(1-t^2)=1.4\\√(1-t^2)=1.4-t\ we\ square\\1-t^2=1.4^2+t^2-2.8*t\\2t^2-2.8*t+0.96=0\\\Delta=2.8^2-4*2*0.96=0.16=0.4^2\\\\t=(2.8-0.4)/(4) =0.6\ or\ t=(2.8+0.4)/(4)=0.8\\\\t^3=0,216\ or\ t^3=0,512\\\\t^5=0,07776\ or\ t^5=0,32768\\\\\boxed{sin(5x)=5*0.6-20*0.216+16*0.07776=-0,07584}\\\\or\\\\\boxed{sin(5x)=5*0.8-20*0.512+16*0.32768=-0,99712}`