What is the general solution for 2cot(x)+3=0 ?

The general solution for 2cot(x)+3=0 is x=2.55359…+pin

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2cot(x)+3=0

2 cot (x) + 3 = 0

x = 2.55359 \dots + πn

Degrees

x = 146.30993 \dots^{\circ} + 18 0^{\circ} n

Solution steps

2 cot (x) + 3 = 0

Move

3

to the right side

2 cot (x) + 3 = 0

Subtract

3

from both sides

2 cot (x) + 3 - 3 = 0 - 3

Simplify

2 cot (x) = - 3

2 cot (x) = - 3

Divide both sides by

2

2 cot (x) = - 3

Divide both sides by

2

\frac{2 cot ( x )}{2} = \frac{- 3}{2}

Simplify

cot (x) = - \frac{3}{2}

cot (x) = - \frac{3}{2}

Apply trig inverse properties

cot (x) = - \frac{3}{2}

General solutions for

cot (x) = - \frac{3}{2}

cot (x) = - a \Rightarrow x = arccot (- a) + πn

x = arccot (- \frac{3}{2}) + πn

x = arccot (- \frac{3}{2}) + πn

Show solutions in decimal form

x = 2.55359 \dots + πn

cos (x + 6 0^{\circ}) + sin (x) = 0

sin (x) \cdot cos (x) = \frac{1}{4}

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

4 sin (θ) + 4 = \frac{- 3}{sin ( θ ) - 1}

cos (θ) = 0.707

What is the general solution for 2cot(x)+3=0 ?
The general solution for 2cot(x)+3=0 is x=2.55359…+pin