This depends on what conventions are used for the Euler Angles. The following are derived on the euler angle page, the first assumes NASA Standard Airplane:
[R] = 

Or, from the same page, this uses NASA Standard Airplane taking angles in the reverse order:
[R] = 

Java code to do conversion:
/** this conversion uses NASA standard aeroplane conventions as described on page: * https://www.euclideanspace.com/maths/geometry/rotations/euler/index.htm * Coordinate System: right hand * Positive angle: right hand * Order of euler angles: [R3][R2][R1] = [about z][about y][about x] = [bank][attitude][heading] * matrix row column ordering: * [m00 m01 m02] * [m10 m11 m12] * [m20 m21 m22]*/ public final void rotate(double heading, double attitude, double bank) {
// Assuming the angles are in radians.
double c1 = Math.cos(heading);
double s1 = Math.sin(heading);
double c2 = Math.cos(attitude);
double s2 = Math.sin(attitude);
double c3 = Math.cos(bank);
double s3 = Math.sin(bank);
m00 = c1 * c2;
m01 = s1 * c2;
m02 = s2;
m10 = s1 * c3+(c1 * s2 * s3);
m11 = (c1*c3)  (s1 * s2 * s3);
m12 = c2 * s3;
m20 = (s1 * s3)  (c1 * s2 * c3);
m21 = (c1 * s3) + (s1 * s2 * c3);
m22 = c2*c3;
}
we take the 90 degree rotation from this:  to this: 
As shown here the axis angle for this rotation is:
heading = 0 degrees
bank = 90 degrees
attitude = 0 degrees
so substituteing this in the above formula gives:
[R] = 

[R] = 

This agrees with the matix rotations here.
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see also: 

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