What is the general solution for cot(x)=-8 ?

The general solution for cot(x)=-8 is x=3.01723…+pin

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cot(x)=-8

cot (x) = - 8

x = 3.01723 \dots + πn

Solution steps

cot (x) = - 8

Apply trig inverse properties

x = arccot (- 8) + πn

Show solutions in decimal form

x = 3.01723 \dots + πn

2 sin (x) cos (x) = cos^{2} (x)

- 1 + sin^{2} (a) + cos^{2} (a) = cos^{2} (a)

\frac{sin ( x )}{1 + cos ( x )} = 3 cot (\frac{x}{2})

sin (θ) = \frac{3}{2}, 0 \leq θ \leq 4 π

sin (2 x) = \frac{3}{2}, 0^{\circ} \leq x \leq 36 0^{\circ}

What is the general solution for cot(x)=-8 ?
The general solution for cot(x)=-8 is x=3.01723…+pin