Unit circle

true randRangeNonZero( -90, 90 ) * 5 ANGLE*2*PI/360 ANGLE + "^{\\circ}" randFromArray( [ "cos", "sin" ] ) { "cos": "cosine", "sin": "sine"}[FN] { "cos": "x", "sin": "y"}[FN] roundTo(3, { "cos": Math.cos(ANGLE * (Math.PI/180)), "sin": Math.sin(ANGLE * (Math.PI/180)) }[FN])

\FN(PRETTY_ANGLE) = \text{?}

SOLUTION

angle

// Convert guess to an angle between 0 and 2*PI for comparison var revolutions = floor(guess / (2 * PI)); var modified_guess = guess - revolutions*2*PI; // Convert answer to an angle between 0 and 2*PI revolutions = floor(ANGLE_RADIANS / (2 * PI)); var modified_angle = ANGLE_RADIANS - revolutions*2*PI; // If the angle is at zero, assume that it was not set. // If the student knows the answer be memory, don't require // them to set the angle. if (abs(guess) < 0.001) return true; // Verify that the angles match return abs( modified_angle - modified_guess ) < 0.001;

KhanUtil.setAngle( guess );

Move the orange point around the unit circle to the angle indicated inside the FNNAME expression above.
Indicate the FNNAME value in the answer field.

initUnitCircle( DEGREES );

To find the FNNAME using the unit circle, first find the angle. Drag the orange point around the circle until PRETTY_ANGLE is selected.

The correct angle is selected. Remember, the FNNAME of an angle is represented by the COORD coordinate of a point on the unit circle.

goToAngle( ANGLE );

The COORD coordinate of the point is SOLUTION, so \FN(PRETTY_ANGLE) = SOLUTION.

goToAngle( ANGLE ); showCoordinates( ANGLE );

false randFromArray([ -6*PI/2, -5*PI/2, -7*PI/3, -9*PI/4, -2*PI, -11*PI/6, -7*PI/4, -5*PI/3, -3*PI/2, -4*PI/3, -5*PI/4, -7*PI/6, -PI, -5*PI/6, -3*PI/4, -2*PI/3, -PI/2, -PI/3, -PI/4, -PI/6, -PI/12, PI/12, PI/6, PI/4, PI/3, PI/2, 2*PI/3, 3*PI/4, 5*PI/6, PI, 7*PI/6, 5*PI/4, 4*PI/3, 3*PI/2, 5*PI/3, 7*PI/4, 11*PI/6, 2*PI, 9*PI/4, 7*PI/3, 5*PI/2, 6*PI/2 ]) ANGLE piFraction(ANGLE) randFromArray( [ "cos", "sin" ] ) { "cos": "cosine", "sin": "sine"}[FN] { "cos": "x", "sin": "y"}[FN] roundTo(3, { "cos": Math.cos(ANGLE), "sin": Math.sin(ANGLE) }[FN])