Final answer:
To find cos 20, use the identity cos^2(a) + sin^2(a) = 1 and the given value of cos 0. To find tan 20, use the identity tan(a) = sin(a)/cos(a).
Step-by-step explanation:
To find cos 20, we can use the identity cos^2(a) + sin^2(a) = 1. Since cos 0 = -(8/17), we can square it to find sin 0. Then, we can use the identity cos(a + b) = cos a cos b - sin a sin b to find cos 20. To find tan 20, we can use the identity tan(a) = sin(a)/cos(a).
Starting with cos 0 = -(8/17), we square it to find sin^2 0 = 1 - cos^2 0 = 1 - ((8/17)^2) = 225/289. Then, we can use the identity cos(a + b) = cos a cos b - sin a sin b to find cos 20 = cos(0 + 20) = cos 0 cos 20 - sin 0 sin 20 = -(8/17)(cos 20) - (15/17)(sin 20). To find tan 20, we can use the identity tan(a) = sin(a)/cos(a) to find tan 20 = sin 20/cos 20.