cos theta = adjacent side / hypotenuse = -4/7 (hyp is always positive).
Thus, the adj. side is -4 when the hyp is 7.
Using the Pyth. Thm. to find the opp side:
(opp side)^2 + (adj side)^2 = (hyp)^2, or
(opp side)^2 + (-4)^2 = 7^2 = 49. Then (opp)^2 +16 = 49, and (opp)^2 = 33.
Then (opp side) = plus or minus sqrt(33)
Because cos theta = -4/7 is negative, theta is in either Quadrant II or Q III.
If in Q II, the opp side will be positive, so the sine of theta is +sqrt(33)/7.
If in Q III, the opp side will be negative, so that the sine of theta is -sqrt(33)/7.
CAN YOU NOW use this info to find tan theta, first for theta in Q II and then for theta in Q III?