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

Answer 1

Given that cos 0 = -5/6, we can use the Pythagorean identity to find sin 0:

sin^2 0 = 1 - cos^2 0
sin^2 0 = 1 - (-5/6)^2
sin^2 0 = 1 - 25/36
sin^2 0 = 11/36
sin 0 = sqrt(11)/6

Since sin 0 is positive and cos 0 is negative, we know that the angle 0 is in the second quadrant. In the second quadrant, tan is positive, so:

tan 0 = sin 0 / cos 0
tan 0 = (sqrt(11)/6) / (-5/6)
tan 0 = -sqrt(11)/5

Therefore, sin 0 = sqrt(11)/6 and tan 0 = -sqrt(11)/5.