The Pythagorean identity is
sin²Ф + cos²Ф=1
or
sin²Ф= 1- cos²Ф
Now in the problem we are given that
cos Ф=3/5
Now to find sin Ф, we can plug the value of cos Ф in the identity
So
sin²Ф= 1- cos²Ф = 1-(3/5)² = 1- 9/25 = (25-9)/25 = 16/25
Sin²Ф= 16/25
take square root on both sides
Now when we take square root on both sides we have to always remember that we will get one positive and one negative answer
So
Sin Ф = 4/5 or -4/5