![\"\"](\"/images/stars/stars-13.gif\")
You can put this solution on YOUR website!
(a) Express 8 Sin theta - 15 Cos theta, in the format: R.Sin(theta + beta)
\n" ); document.write( "LET US USE T FOR THETA AND B FOR BETA
\n" ); document.write( "DIVIDE AND MULTIPLY WITH SQRT(8^2+15^2)=17
\n" ); document.write( "PUT 8/17=COS(B)....THEN.....15/17=SIN(B)...SINCE SIN(B)=SQRT[1-COS^2(B)
\n" ); document.write( "=SQRT[1-(8/17)^2]=15/17
\n" ); document.write( "HENCE WE GET
\n" ); document.write( "8SIN(T)-15COS(B)=17[(8/17)SIN(T)-(15/17)COS(T)]
\n" ); document.write( "=17[SIN(T)COS(B)-COS(T)SIN(B)]=17SIN[T-B]..
\n" ); document.write( "HENCE R=17 AND B=ARCSIN(15/17)
\n" ); document.write( "IF YOU WANT ONLY SIN (T+B)THEN YOU HAVE TO CHANGE THE QUADRANT
\n" ); document.write( "FOR THE ANGLE FROM I Q AT PRESENT.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "(b) Using your answer to part (a), solve; 8 Sin theta - 15 Cos theta=8.5 for 0degrees<=theta<=360degrees
\n" ); document.write( "WE HAVE
\n" ); document.write( "17SIN(T-B)=8.5
\n" ); document.write( "SIN(T-B)=8.5/17=1/2=SIN(30)....OR....SIN(150).....OR...SIN(390)...ETC
\n" ); document.write( "T-B=30....OR....150...OR....390...0R....510...ETC
\n" ); document.write( "BUT B = ARCSIN(15/17)=62 DEG.
\n" ); document.write( "T=92...OR.....212...IN THE DESIRED RANGE OF 0
\n" ); document.write( "T