document.write( "Question 1088220: the max value of sin(x+π/6)+cos(x+π÷6)in the intervals (0,π÷2)is attained at \n" ); document.write( "

Algebra.Com's Answer #702473 by natolino_2017(77) $\"\"$ $\"About$

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let f(x) = sin(x+π/6)+cos(x+π÷6)\r
\n" ); document.write( "\n" ); document.write( "so f'(x) = cos(x+π/6)-sin(x+π÷6) = 0\r
\n" ); document.write( "\n" ); document.write( " tan(x+π/6) = 1 so x = π÷12\r
\n" ); document.write( "\n" ); document.write( "Which is stationary point.\r
\n" ); document.write( "\n" ); document.write( "also frontier's poitns are candidate.\r
\n" ); document.write( "\n" ); document.write( "f(0) = 1/2 +sqrt(3)/2 = (1+sqrt(3))/2.\r
\n" ); document.write( "\n" ); document.write( "f(π÷2) = sin(2π/3)+cos(2π/3) = sqrt(3)/2 -1/2 = (sqrt(3)-1)/2 (min).\r
\n" ); document.write( "\n" ); document.write( "f(π÷12) = sin(π/4)+cos(π/4) = sqrt(2)/2+sqrt(2)/2 = sqrt(2) (max).\r
\n" ); document.write( "\n" ); document.write( "Max is sqrt(2), Min is (sqrt(3)-1)/2, all this not using
\n" ); document.write( "sinusoid's properties. \n" ); document.write( "

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