Final answer:
To find the value of cot(theta), we need to find the value of cos(theta) using the Pythagorean identity. Then we can calculate cot(theta) by taking the reciprocal of tan(theta). The value of cot(theta) is 4/3.
Step-by-step explanation:
To find the value of cot(theta), we need to use the relationship between the trigonometric functions. Since sin(theta) = 3/5 and theta lies in quadrant 2, we can determine the value of cos(theta) using the Pythagorean identity. The Pythagorean identity states that sin^2(theta) + cos^2(theta) = 1. Therefore, cos^2(theta) = 1 - sin^2(theta) = 1 - (3/5)^2 = 1 - 9/25 = 16/25. Taking the square root of both sides gives cos(theta) = 4/5.
Now we can calculate the value of cot(theta) by taking the reciprocal of tan(theta). Since tan(theta) = sin(theta)/cos(theta), cot(theta) is equal to cos(theta)/sin(theta). Substituting the values, cot(theta) = (4/5)/(3/5) = 4/3.