Remark The cot(theta) = 4/7 That means we have an adjacent of 4 and an opposite of 7. We still need to find the hypotenuse.
Step One Find the hypotenuse a^2 + b^2 = c^2 a = 4 b = 7 c = ??? 4^2 + 7^2 = c^2 c^2 = 16 + 49 c^2 = 65 Take the square root of both sides. c = sqrt(65)
Now find Sin(theta) Sin(theta) = 7/ sqrt(65)
The other way to do it would be to solve cot^2(theta) + 1 = csc^2(theta) (4/7)^2 + 1 = csc^2(theta) 16/49 + 1 = csc^2 (theta) 65/49 =csc^2(theta)
sqrt(65)/7 = csc(theta) 7 / sqrt(65) = sin(theta)
There's a choice of two ways to do it. The first way is using cot = adjacent /opposite.
The second is using 1 + cot^2(theta) = csc^2(theta) and sin(theta) = 1 / csc(theta).
