promotion image of download ymail app
Promoted

Hello,  I do not know how to solve for the smallest positive solutions. Can anyone please help?

Attachment image

2 Answers

Relevance
  • 2 months ago
    Favorite Answer

    sin(3x)cos(8x) - cos(3x)sin(8x) = -0.85 

    remember 

    sin(a-b) = sin(a)cos(b) - cos(a)sin(b)

    so the 15 equation is equivalent to 

    sin(3x-8x) = sin(-5x) = -0.85   

    sin(-5x) =-sin(5x) = -0.85 

    sin(5x) = 0.85       

    asin(0.85)  =  1.015985294   

    plus since 

    sin(x) = sin(pi-x)  

    asin(0.85) gvies   1.015985294    or 

    2.12560736

    Remember sine and cosine  

    have a period of 2pi  

    5x = 1.015985294 + 2pik   where k is an integer

    x = (1.015985294/5) + (2/5)pik

    x=     0.203197059    + (2/5)*pik 

    since (2/5)pi is greater than 0.2032  

    k = 0 is the smallest 

    x =  0.203197059

    or 

    5x =  2.12560736   + 2pik 

    x = (2.12560736/5) + (2/5)pik 

    x=  0.425121472 + (2/5)*pik 

    since (2/5)pi is greater than 0.42512

    x= 0.425121472  

    so 

    x = 0.203197059

    is the smallest solution

    • Savannah2 months agoReport

      Thank you sooooo much Alvin!

    • Commenter avatarLogin to reply the answers
  • 2 months ago

    By Trig. Identity 

    Sin( 3 x - 8x) => 

    Sin (-5x) = -0.85

    -5x = Sin^-1(-0.85radians)

    -5x = -1.015985...

    5x = 1.015985.... 

    x = 1.015985../ 5 = 0.203197 

    • Commenter avatarLogin to reply the answers
Still have questions? Get your answers by asking now.