Answer:
Since cos 0 is positive (i.e. √2/5 > 0), we know that 0 is in the first or fourth quadrant of the unit circle.
Since sin 0 is negative (i.e. sin 0 < 0), we know that 0 is in the third or fourth quadrant of the unit circle.
In the first quadrant, both sine and cosine are positive, so that cannot be the case.
Therefore, 0 must be in the fourth quadrant of the unit circle, where cosine is positive and sine is negative.
Using the Pythagorean identity, we can find the value of sine:
sin^2 0 + cos^2 0 = 1
sin^2 0 + (√2/5)^2 = 1
sin^2 0 + 2/5 = 1
sin^2 0 = 3/5
sin 0 = ±√(3/5)
Since we know that sin 0 is negative, we take the negative root:
sin 0 = -√(3/5)
Therefore, the value of sin 0 is -√(3/5).
- I Hope This Helps! :)