What is the general solution for 3tan(θ)+2cos(θ)=0 ?

The general solution for 3tan(θ)+2cos(θ)=0 is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin

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3tan(θ)+2cos(θ)=0

3 tan (θ) + 2 cos (θ) = 0

θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Solution steps

3 tan (θ) + 2 cos (θ) = 0

Express with sin, cos

\frac{2 cos ^{2} ( θ ) + 3 sin ( θ )}{cos ( θ )} = 0

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

2 cos^{2} (θ) + 3 sin (θ) = 0

Rewrite using trig identities

(1 - sin^{2} (θ)) \cdot 2 + 3 sin (θ) = 0

Solve by substitution

sin (θ) = - \frac{1}{2}, sin (θ) = 2

sin (θ) = - \frac{1}{2} : θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

sin (θ) = 2 :

No Solution

Combine all the solutions

θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

9 + cot^{2} (x) = 12

cos (a) = 0.8

cos (a) = 0.6

5 cos^{2} (θ) = 6 sin (θ)

8 tan (θ) = 0

What is the general solution for 3tan(θ)+2cos(θ)=0 ?
The general solution for 3tan(θ)+2cos(θ)=0 is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin