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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

1/(sec(θ))=-7/25

\frac{1}{sec ( θ )} = - \frac{7}{25}

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

Degrees

θ = 106.26020 \dots^{\circ} + 36 0^{\circ} n, θ = - 106.26020 \dots^{\circ} + 36 0^{\circ} n

Solution steps

\frac{1}{sec ( θ )} = - \frac{7}{25}

Cross multiply

\frac{1}{sec ( θ )} = - \frac{7}{25}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

1 \cdot 25 = - sec (θ) \cdot 7

Simplify

1 \cdot 25 : 25

1 \cdot 25

Multiply the numbers:

1 \cdot 25 = 25

= 25

25 = - sec (θ) \cdot 7

25 = - sec (θ) \cdot 7

Switch sides

- sec (θ) \cdot 7 = 25

Divide both sides by

- 7

- sec (θ) \cdot 7 = 25

Divide both sides by

- 7

\frac{- sec ( θ ) \cdot 7}{- 7} = \frac{25}{- 7}

Simplify

sec (θ) = - \frac{25}{7}

sec (θ) = - \frac{25}{7}

Verify Solutions

Find undefined (singularity) points:

sec (θ) = 0

Take the denominator(s) of

\frac{1}{sec ( θ )}

and compare to zero

sec (θ) = 0

The following points are undefined

sec (θ) = 0

Combine undefined points with solutions:

sec (θ) = - \frac{25}{7}

Apply trig inverse properties

sec (θ) = - \frac{25}{7}

General solutions for

sec (θ) = - \frac{25}{7}

sec (x) = - a \Rightarrow x = arcsec (- a) + 2 πn, x = - arcsec (- a) + 2 πn

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

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