Given cot = -7/4
cot Θ = 1/tan Θ
tan Θ^2+1 = sec Θ^2
1+cot Θ^2 = cosec Θ^2
cosec Θ = 1/sinΘ
-7/4 = 1/tan Θ
tan Θ = 4/7
(4/7)^2+1 = sec Θ^2
16/49+1 = sec Θ^2
16/49+49/49 = sec Θ^2
65/49 = sec Θ^2
sec Θ = √65/7
1+(-7/2)^2 = cosec Θ^2
16/16 + 49/16 = cosec Θ^2
65/16 = cosec Θ^2
cosec Θ = √65/16
√65/16 = 1/sin Θ
sin Θ = √16/65
If I did this right, those should be the answers. I'm a little rusty, but I hope this helps.
-Ivy
