Unfortunately, the radio trigger in the YN-560 IV can only communicate with other Yongnuo flashes/receivers. (i.e. YN-560 IV, YN-560 III, YN560-TX, RF-603 (I/II), and RF-602)
That said, the YN-560 IV
does have a built in Slave mode that will allow you to use it off-camera by triggering it from your K-3's on-board flash. Set your YN-560 IV to S1 or S2 mode, and point the little red window on the flash towards your K-3. When your K-3's flash fires, your YN-560 will flash too.
Alternatively, you can buy the RF-603 I/II on
B&H. It communicates wirelessly with your YN-560 IV so you don't have to rely on line-of-sight control.