Question

If the cos 0=3/5 use the Pythagorean identity to find sin 6

Answer 1

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