Final answer:
To find sin(x) and cos(x), we can use the given information that tan(x) = 1/5 and sin(x) > 0. By plugging these values into trigonometric identities, we can find the values of sin(x) and cos(x).
Step-by-step explanation:
To find sin(x) and cos(x), we need to use the given information that tan(x) = 1/5 and sin(x) > 0.
First, we can determine the value of cos(x) using the identity tan(x) = sin(x)/cos(x). Plugging in tan(x) = 1/5, we get 1/5 = sin(x)/cos(x). Cross multiplying, we have sin(x) = cos(x)/5.
Next, since sin(x) > 0, we know that cos(x) must also be positive. From the equation sin(x) = cos(x)/5, we can see that the only way for sin(x) to be positive while cos(x) is positive is if both sin(x) and cos(x) are positive. Therefore, sin(x) = cos(x)/5, cos(x) = 5*sin(x).