document.write( "Question 924929: Suppose cos(t)=-1/3 and sin(t)<0 Use appropriate identities to find each of the following?
\n" ); document.write( "sec(-1) \r
\n" ); document.write( "\n" ); document.write( "sin(-t) \r
\n" ); document.write( "\n" ); document.write( "cos(t+5π/3) \r
\n" ); document.write( "\n" ); document.write( "sin(2t) \r
\n" ); document.write( "\n" ); document.write( "Please give details I have to understand \r
\n" ); document.write( "\n" ); document.write( "Thanks! \n" ); document.write( "

Algebra.Com's Answer #561287 by lwsshak3(11628) $\"\"$ $\"About$

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Suppose cos(t)=-1/3 and sin(t)<0 Use appropriate identities to find each of the following?
\n" ); document.write( "sec(-1)
\n" ); document.write( "sin(-t)
\n" ); document.write( "cos(t+5π/3)
\n" ); document.write( "sin(2t)
\n" ); document.write( "***
\n" ); document.write( "cos(t)=-1/3
\n" ); document.write( "sin(t)<0
\n" ); document.write( "reference angle t is in quadrant III where sin<0, cos<0
\n" ); document.write( "sin(t)=-√(1-cos^2(t))=-√(1-1/9)=-√(8/9)=-√8/3
\n" ); document.write( "..
\n" ); document.write( "sec(-1)=1/cos(-1)=1/-0.54≈-1.85
\n" ); document.write( "note:(reference angle=1(radian) in quadrant IV where sin<0)
\n" ); document.write( "sin(-t)=-sin(t)=-√8/3
\n" ); document.write( "cos(t+5π/3)=cos(t)*cos(5π/3)-sin(t)*sin(5π/3)
\n" ); document.write( "=-1/3*1/2-(-√8/3)*(-√3/2)=-1/6-√24/6=-(1+√24)/6
\n" ); document.write( "..
\n" ); document.write( "sin(2t)=2*sin(t)*cos(t)=2*-√8/3*-1/3=2√8/9 \n" ); document.write( "

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