document.write( "Question 722988: Use the trigonometric substitution to write the algebraic equation as a trigonometric equation of θ, where −π/2 < θ < π/2.
\n" ); document.write( "(4 = sqrt (64 − x^2)) , x = 8 sin θ \r
\n" ); document.write( "\n" ); document.write( "4=?\r
\n" ); document.write( "\n" ); document.write( "Find sin θ and cos θ. \r
\n" ); document.write( "\n" ); document.write( "sin θ= ?
\n" ); document.write( "cos θ=? \n" ); document.write( "

Algebra.Com's Answer #442971 by stanbon(75887) $\"\"$ $\"About$

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Use the trigonometric substitution to write the algebraic equation as a trigonometric equation of θ, where −π/2 < θ < π/2.
\n" ); document.write( "(4 = sqrt (64 − x^2)) , x = 8 sin θ
\n" ); document.write( "16 = 64-x^2
\n" ); document.write( "x^2 = 32
\n" ); document.write( "x = 4sqrt(2) or x = -4sqrt(2)
\n" ); document.write( "-----
\n" ); document.write( "Substitute for \"x\":
\n" ); document.write( "8sin(theta) = 4sqrt(2) or 8sin(theta) = -4sqrt(2)
\n" ); document.write( "---------------------
\n" ); document.write( "sin(theta) = sqrt(2)/2; and cos(theta) = sqrt(2/2) in QI
\n" ); document.write( "or sin(theta) = -sqrt(2)/2 and cos(theta) = sqrt(2)/2) in QIV
\n" ); document.write( "======================
\n" ); document.write( "Find sin θ and cos θ.
\n" ); document.write( "sin θ= ?
\n" ); document.write( "cos θ=?\r
\n" ); document.write( "\n" ); document.write( "======
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

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