cot theta= -5/4, cos theta<0 find csc theta
the answer is: sqrt41/4
the answer is: sqrt41/4
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On the coordinate plane sin θ= y/r and cos θ= x/r
the tan θ= y/x
The cotθ = 1/tanθ = x/y= -5/4
since to cos θ <1 and the cot θ < 1 (both negative ) because x = -4 and y=5
we must be in QII and the sin θ and csc θ are both positive in QII
x^2 + y^2 = r^2
(-4)^2 + (5)^2 = r^2
16 + 25 = r^2
41 = r^2
r = √41
sin θ = y/r so the csc θ = r/y = √41/4
the tan θ= y/x
The cotθ = 1/tanθ = x/y= -5/4
since to cos θ <1 and the cot θ < 1 (both negative ) because x = -4 and y=5
we must be in QII and the sin θ and csc θ are both positive in QII
x^2 + y^2 = r^2
(-4)^2 + (5)^2 = r^2
16 + 25 = r^2
41 = r^2
r = √41
sin θ = y/r so the csc θ = r/y = √41/4