What is the general solution for 2csc(θ)+3sec(θ)=0 ?

The general solution for 2csc(θ)+3sec(θ)=0 is θ=-0.58800…+pin

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2csc(θ)+3sec(θ)=0

2 csc (θ) + 3 sec (θ) = 0

θ = - 0.58800 \dots + πn

Solution steps

2 csc (θ) + 3 sec (θ) = 0

Express with sin, cos

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

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

2 cos (θ) + 3 sin (θ) = 0

Rewrite using trig identities

2 + 3 tan (θ) = 0

Move

2

to the right side

3 tan (θ) = - 2

Divide both sides by

3

tan (θ) = - \frac{2}{3}

Apply trig inverse properties

θ = arctan (- \frac{2}{3}) + πn

Show solutions in decimal form

θ = - 0.58800 \dots + πn

6 + 9 cos (x) = 2 sin^{2} (x)

tan (2 θ) = \frac{77}{51 - 20}

2 - 7 cos (x) = 0

cos (θ) = - \frac{8}{17}

cos (2 x) = 8 - 15 sin (x)

What is the general solution for 2csc(θ)+3sec(θ)=0 ?
The general solution for 2csc(θ)+3sec(θ)=0 is θ=-0.58800…+pin