Explanation:
We can use the Pythagorean identity to solve for the missing values of sin(theta) and cos(theta) given the value of tangent(theta):
tan(theta) = opposite/adjacent = sin(theta) / cos(theta)
Using the given value of tan(theta) = 12/5, we can assume that the opposite side of the right triangle is 12 and the adjacent side is 5.
Then we can solve for the missing values of sin(theta) and cos(theta) using the Pythagorean theorem:
hypotenuse^2 = opposite^2 + adjacent^2 sin(theta)^2 + cos(theta)^2 = 1
Solving for sin(theta) and cos(theta), we get:
sin(theta) = opposite/hypotenuse = 12/13 cos(theta) = adjacent/hypotenuse = 5/13
Therefore, sin(theta) = 12/13 and cos(theta) = 5/13.