To find the sine of an angle bigger than 90°, but less than 360° you need to find out which quadrant the angle is in. This determines the sign (+ or -) of the sine of the angle and also reduces the angle so that's in the first quadrant (0-90°). The second quadrant deals with angles between 90° and 180°; the third quadrant between 180° and 270°; and the fourth quadrant between 270° and 360°.
230° is in the third quadrant. In this quadrant the sine function is negative and the angle is reduced by 180°, so we need -sin(230-180)=-sin(50)=-0.7660 approx.
Using Q for quadrant, we have the rule ASTC (all-sin-tan-cos) for Q1 to Q4 respectively. This acronym tells us which of the trig functions are positive in each quadrant (all others being negative in the same quadrant). A useful mnemonic for ASTC is "all silver teacups".
For angles bigger than 360° keep subtracting 360° until the angle lies between 0° and 360°, then work out which quadrant it's in.
For negative angles, keep adding 360° until it becomes positive, then work out which quadrant it's in.