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Strafing left and right

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What is the formula to strafe left or right?
In the following code fragment, FORWARD and BACKWARD work perfectly but LEFT and RIGHT only work properly when the angle is 0, PI/2, PI, 3PI/2 or 2PI. Another thing I noticed is that when the angle is PI/4, 3PI/4, 5PI/4 or 7PI/4 and I hold down FORWARD and LEFT or BACK and RIGHT the camera strafes left and right properly. I am useing a fixed cordinate system with the camera moving parallel to the x and z plane.

switch (key)
{
< >case FORWARD:
< >cameraz -= cos(angle);
< >camerax += sin(angle);
< >glutPostRedisplay();
< >break;
< >case BACK:
< >cameraz += cos(angle);
< >camerax -= sin(angle);
< >glutPostRedisplay();
< >break;
< >case LEFT:
< >cameraz += sin(angle);
< >camerax -= cos(angle);
< >glutPostRedisplay();
< >break;
< >case RIGHT:
< >cameraz -= sin(angle);
< >camerax += cos(angle);
< >glutPostRedisplay();
< >break;
< >default:
< >break;
}

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