What is the general solution for sec(x/5)=sqrt(10) ?

The general solution for sec(x/5)=sqrt(10) is x=5*1.24904…+10pin,x=10pi-5*1.24904…+10pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sec(x/5)=sqrt(10)

sec (\frac{x}{5}) = 10

x = 5 \cdot 1.24904 \dots + 10 πn, x = 10 π - 5 \cdot 1.24904 \dots + 10 πn

Degrees

x = 357.82525 \dots^{\circ} + 180 0^{\circ} n, x = 1442.17474 \dots^{\circ} + 180 0^{\circ} n

Solution steps

sec (\frac{x}{5}) = 10

Apply trig inverse properties

sec (\frac{x}{5}) = 10

General solutions for

sec (\frac{x}{5}) = 10

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

\frac{x}{5} = arcsec (10) + 2 πn, \frac{x}{5} = 2 π - arcsec (10) + 2 πn

\frac{x}{5} = arcsec (10) + 2 πn, \frac{x}{5} = 2 π - arcsec (10) + 2 πn

Solve

\frac{x}{5} = arcsec (10) + 2 πn : x = 5 arcsec (10) + 10 πn

\frac{x}{5} = arcsec (10) + 2 πn

Multiply both sides by

5

\frac{x}{5} = arcsec (10) + 2 πn

Multiply both sides by

5

\frac{5 x}{5} = 5 arcsec (10) + 5 \cdot 2 πn

Simplify

\frac{5 x}{5} = 5 arcsec (10) + 5 \cdot 2 πn

Simplify

\frac{5 x}{5} : x

\frac{5 x}{5}

Divide the numbers:

\frac{5}{5} = 1

= x

Simplify

5 arcsec (10) + 5 \cdot 2 πn : 5 arcsec (10) + 10 πn

5 arcsec (10) + 5 \cdot 2 πn

Multiply the numbers:

5 \cdot 2 = 10

= 5 arcsec (10) + 10 πn

x = 5 arcsec (10) + 10 πn

x = 5 arcsec (10) + 10 πn

x = 5 arcsec (10) + 10 πn

Solve

\frac{x}{5} = 2 π - arcsec (10) + 2 πn : x = 10 π - 5 arcsec (10) + 10 πn

\frac{x}{5} = 2 π - arcsec (10) + 2 πn

Multiply both sides by

5

\frac{x}{5} = 2 π - arcsec (10) + 2 πn

Multiply both sides by

5

\frac{5 x}{5} = 5 \cdot 2 π - 5 arcsec (10) + 5 \cdot 2 πn

Simplify

\frac{5 x}{5} = 5 \cdot 2 π - 5 arcsec (10) + 5 \cdot 2 πn

Simplify

\frac{5 x}{5} : x

\frac{5 x}{5}

Divide the numbers:

\frac{5}{5} = 1

= x

Simplify

5 \cdot 2 π - 5 arcsec (10) + 5 \cdot 2 πn : 10 π - 5 arcsec (10) + 10 πn

5 \cdot 2 π - 5 arcsec (10) + 5 \cdot 2 πn

Multiply the numbers:

5 \cdot 2 = 10

= 10 π - 5 arcsec (10) + 10 πn

x = 10 π - 5 arcsec (10) + 10 πn

x = 10 π - 5 arcsec (10) + 10 πn

x = 10 π - 5 arcsec (10) + 10 πn

x = 5 arcsec (10) + 10 πn, x = 10 π - 5 arcsec (10) + 10 πn

Show solutions in decimal form

x = 5 \cdot 1.24904 \dots + 10 πn, x = 10 π - 5 \cdot 1.24904 \dots + 10 πn

csc (x) = - 3

csc (x) = - 5

csc^{2} (θ) + 1 = cot^{2} (θ)

csc^{2} (θ) = 1

sin^{2} (θ) = cos^{2} (θ) - 1

What is the general solution for sec(x/5)=sqrt(10) ?
The general solution for sec(x/5)=sqrt(10) is x=5*1.24904…+10pin,x=10pi-5*1.24904…+10pin