What is the general solution for 1/(sec(θ))=-7/25 ?

The general solution for 1/(sec(θ))=-7/25 is θ=1.85459…+2pin,θ=-1.85459…+2pin

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1/(sec(θ))=-7/25

\frac{1}{sec ( θ )} = - \frac{7}{25}

θ = 1.85459 \dots + 2 πn, θ = - 1.85459 \dots + 2 πn

Solution steps

\frac{1}{sec ( θ )} = - \frac{7}{25}

Cross multiply

25 = - sec (θ) \cdot 7

Switch sides

- sec (θ) \cdot 7 = 25

Divide both sides by

- 7

sec (θ) = - \frac{25}{7}

Verify Solutions

Find undefined (singularity) points:

sec (θ) = 0

Combine undefined points with solutions:

sec (θ) = - \frac{25}{7}

Apply trig inverse properties

θ = arcsec (- \frac{25}{7}) + 2 πn, θ = - arcsec (- \frac{25}{7}) + 2 πn

Show solutions in decimal form

θ = 1.85459 \dots + 2 πn, θ = - 1.85459 \dots + 2 πn

3 tan^{3} (x) - 2 tan^{2} (x) - 32 tan (x) - 32 = 0

x, 2 sin (5 x) - 1 = 0

cos (\frac{x}{2}) = \frac{1}{2}

2 \cdot cos (2 x) + 1 = 0

sin (2 x) - cos^{2} (x) = 0

What is the general solution for 1/(sec(θ))=-7/25 ?
The general solution for 1/(sec(θ))=-7/25 is θ=1.85459…+2pin,θ=-1.85459…+2pin