Find sin 0 and tan 0, given cos 0 = - 5/6 and sin 0 > 0

Answer 1

Since sin 0 is positive and cos 0 is negative, we are in the second quadrant.

Using the Pythagorean identity sin^2θ + cos^2θ = 1, we have:

sin^2θ + (-5/6)^2 = 1
sin^2θ + 25/36 = 1
sin^2θ = 1 - 25/36
sin^2θ = 11/36
sinθ = √(11/36)
sinθ = √11 / 6

Now we can find tanθ:

tanθ = sinθ / cosθ
tanθ = (√11 / 6) / (-5/6)
tanθ = (√11) / (-5)

Therefore, sin 0 = √11 / 6 and tan 0 = -√11 / 5.