document.write( "Question 943297: Angle a is in the second quadrant with sin a= 2/5 and angle b= pi/ 6.
\n" ); document.write( "find sin(a+b) and cos(a+b). What quadrant is a+b in?
\n" ); document.write( "Find sin (a-b) and cos(a-b). What quadrant is a-b in?\r
\n" ); document.write( "\n" ); document.write( "(If you can help me with the sin and cos of a+b, I can probably figure the others out on my own). \n" ); document.write( "
Algebra.Com's Answer #575199 by lwsshak3(11628)\"\" \"About 
You can put this solution on YOUR website!
Angle a is in the second quadrant with sin a= 2/5 and angle b= pi/ 6.
\n" ); document.write( "find sin(a+b) and cos(a+b). What quadrant is a+b in?
\n" ); document.write( "***
\n" ); document.write( "sina=2/5
\n" ); document.write( "cosa=-√(1-sin^2(a))=-√(1-4/25)=-√(21/25)=-√21/5
\n" ); document.write( "sinb=1/2
\n" ); document.write( "cosb=√3/2
\n" ); document.write( "sin(a+b)=sina*cosb+cosa*sinb=2/5*√3/2+-√21/5*1/2=2√3/10-√21/10=(2√3-√21)/10
\n" ); document.write( "cos(a+b)=cosa*cosb-sina*sinb=-√21/5*√3/2-2/5*1/2=-√63/10-2/10=-(√63+2)/10
\n" ); document.write( "Check:w/calculator
\n" ); document.write( "sina=2/5
\n" ); document.write( "a=156.42˚
\n" ); document.write( "b=30˚
\n" ); document.write( "a+b=186.42 (Quadrant II)
\n" ); document.write( "sin(a+b)=sin(186.42)≈-0.1118..
\n" ); document.write( "exact value=(2√3-√21)/10≈-0.1118..
\n" ); document.write( "..
\n" ); document.write( "cos(a+b)=cos(186.42)≈-0.9937..
\n" ); document.write( "exact value=-(√63+2)/10≈-0.9937.. \n" ); document.write( "
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