This exercise covers inverses of trig functions.
random() < 0.5
random() < 0.5
randFromArray([ "sin", "cos", "tan" ])
"\\" + FN + "^{-1}"
"\\arc" + FN
function( x, arc ) {
return ( ( typeof arc === "undefined" ? ARC : arc ) ? FN_ARC : FN_INV ) + "\\left(" + x + "\\right)";
}
[ 0, 1/2, sqrt(2)/2, sqrt(3)/2 ]
[ 0, sqrt(3)/3, 1, sqrt(3) ]
( random() < 0.5 ? -1 : 1 ) * {
sin: randFromArray( SIN_RANGE ),
cos: randFromArray( SIN_RANGE ),
tan: randFromArray( TAN_RANGE )
}[ FN ]
{
sin: asin,
cos: acos,
tan: atan
}[ FN ]( X )
round( Y * 180 / PI )
KhanUtil.toFraction( Y / Math.PI, 0.001 )
( Y_DEGREES === 0 ? "^(\\s*0*\\s*)|" : "^" ) + Y_DEGREES + "\\s*[Dd][Ee][Gg]([Rr][Ee][Ee][Ss])?\\s*$"
function( n ) {
var sign = n < 0 ? "-" : "";
n = abs( n );
var o = {};
o[ 1/2 ] = "\\frac{1}{2}";
o[ sqrt(2)/2 ] = "\\frac{\\sqrt{2}}{2}";
o[ sqrt(3)/2 ] = "\\frac{\\sqrt{3}}{2}";
o[ sqrt(3)/3 ] = "\\frac{\\sqrt{3}}{3}";
o[ sqrt(3) ] = "\\sqrt{3}";
return sign + ( o[n] || n );
}
{
sin: [ DEG ? "-90°" : "-\\frac{\\pi}{2}", DEG ? "90°" : "\\frac{\\pi}{2}" ],
cos: [ "0", DEG ? "180°" : "\\pi" ],
tan: [ DEG ? "-90°" : "-\\frac{\\pi}{2}", DEG ? "90°" : "\\frac{\\pi}{2}" ]
}[ FN ]
What is the principal value of FN_TEX( PRETTY( X ) )?
Note: please answer in terms of degrees (ex: "180 deg" or "180 degrees")radians (ex: "3/4 pi").
FN_TEX( PRETTY( X ) ) = FN_TEX( PRETTY( X ), false )
If FN_TEX( PRETTY( X ), false ) = \theta, then...
"\\" + FN\left( \theta \right) = PRETTY( X )
The range of FN_TEX( "x" ) is [ DOMAIN[0], DOMAIN[1] ], so we know DOMAIN[0] \leq \theta \leq DOMAIN[1].
"\\" + FN \left( fractionReduce( Y_RADIANS[0], Y_RADIANS[1], true )\pi \right) = PRETTY( X )
fractionReduce( Y_RADIANS[0], Y_RADIANS[1], true )\pi\mbox{ (radians) }=Y_DEGREES °
So FN_TEX( PRETTY( X ) ) = DEG ? Y_DEGREES + "°" : fractionReduce( Y_RADIANS[0], Y_RADIANS[1], true ) + "\\pi".