What is the general solution for sin(θ)cot(θ)=(sqrt(3))/2 ?

The general solution for sin(θ)cot(θ)=(sqrt(3))/2 is θ= pi/6+2pin,θ=(11pi)/6+2pin

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sin(θ)cot(θ)=(sqrt(3))/2

sin (θ) cot (θ) = \frac{3}{2}

θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Solution steps

sin (θ) cot (θ) = \frac{3}{2}

Subtract

\frac{3}{2}

from both sides

sin (θ) cot (θ) - \frac{3}{2} = 0

Simplify

sin (θ) cot (θ) - \frac{3}{2} : \frac{2 sin ( θ ) cot ( θ ) - 3}{2}

\frac{2 sin ( θ ) cot ( θ ) - 3}{2} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

2 sin (θ) cot (θ) - 3 = 0

Rewrite using trig identities

- 3 + 2 cos (θ) = 0

Move

3

to the right side

2 cos (θ) = 3

Divide both sides by

2

cos (θ) = \frac{3}{2}

General solutions for

cos (θ) = \frac{3}{2}

θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

cos^{2} (θ) + \frac{1 0 ^{2}}{9.81 ( 1 )} cos (θ) - 1 = 0

cos^{4} (x) = \frac{1}{16}

w, P = 4 (\frac{Y}{P sin ( w )})

tan (2 θ) = \frac{500}{350 - 75}

sec (a) = - 2

What is the general solution for sin(θ)cot(θ)=(sqrt(3))/2 ?
The general solution for sin(θ)cot(θ)=(sqrt(3))/2 is θ= pi/6+2pin,θ=(11pi)/6+2pin