Final answer:
To find sin(x) and tan(x), we can use the given value of cos(x)=-12/13, which implies that x is in the second quadrant. In the second quadrant, sin(x) is positive and tan(x) is negative. Using the Pythagorean identity and the unit circle, we can find sin(x) = 5/13 and tan(x) = -5/12.
Step-by-step explanation:
To find the other two trigonometric functions, we can use the given value of cos(x) and the unit circle. Since cos(x) = -12/13 is negative, we know that x is in the second quadrant. In the second quadrant, sin(x) is positive and tan(x) is negative. Using the Pythagorean identity, we can find sin(x) by finding the length of the opposite side in the unit circle: sin(x) = sqrt(1 - cos^2(x)) = sqrt(1 - (-12/13)^2) = sqrt(1 - 144/169) = sqrt(169 - 144)/13 = 5/13. Finally, we can find tan(x) by dividing sin(x) by cos(x): tan(x) = sin(x)/cos(x) = (5/13)/(-12/13) = -5/12.