Final answer:
To find the values of sin(a) and tan(a) when cos(a) = 5/13, we can use the Pythagorean identity sin^2(a) + cos^2(a) = 1. By rearranging the equation and substituting the given value, we can find sin(a). To find tan(a), we can use the relationship tan(a) = sin(a)/cos(a).
Step-by-step explanation:
To find the values of sin(a) and tan(a), we can use the given value of cos(a) = 5/13. Since cosine is positive in the first and fourth quadrants, we know that the angle a is in either the first or fourth quadrant. Using the Pythagorean identity, sin^2(a) + cos^2(a) = 1, we can find sin(a) by rearranging the equation and substituting the value of cos(a): sin^2(a) = 1 - cos^2(a) = 1 - (5/13)^2. Taking the square root of both sides, we find sin(a) = ±sqrt(1 - (5/13)^2). To find the value of tan(a), we can use the relationship tan(a) = sin(a)/cos(a). Therefore, the values of sin(a) are ±sqrt(1 - (5/13)^2) and the value of tan(a) is ±sqrt(1 - (5/13)^2) / (5/13) = ±sqrt(1 - (5/13)^2) * 13/5.