What is the general solution for sec(θ/5)=sqrt(7) ?

The general solution for sec(θ/5)=sqrt(7) is θ=5*1.18319…+10pin,θ=10pi-5*1.18319…+10pin

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sec(θ/5)=sqrt(7)

sec (\frac{θ}{5}) = 7

θ = 5 \cdot 1.18319 \dots + 10 πn, θ = 10 π - 5 \cdot 1.18319 \dots + 10 πn

Degrees

θ = 338.96172 \dots^{\circ} + 180 0^{\circ} n, θ = 1461.03827 \dots^{\circ} + 180 0^{\circ} n

Solution steps

sec (\frac{θ}{5}) = 7

Apply trig inverse properties

sec (\frac{θ}{5}) = 7

General solutions for

sec (\frac{θ}{5}) = 7

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

\frac{θ}{5} = arcsec (7) + 2 πn, \frac{θ}{5} = 2 π - arcsec (7) + 2 πn

\frac{θ}{5} = arcsec (7) + 2 πn, \frac{θ}{5} = 2 π - arcsec (7) + 2 πn

Solve

\frac{θ}{5} = arcsec (7) + 2 πn : θ = 5 arcsec (7) + 10 πn

\frac{θ}{5} = arcsec (7) + 2 πn

Multiply both sides by

5

\frac{θ}{5} = arcsec (7) + 2 πn

Multiply both sides by

5

\frac{5 θ}{5} = 5 arcsec (7) + 5 \cdot 2 πn

Simplify

\frac{5 θ}{5} = 5 arcsec (7) + 5 \cdot 2 πn

Simplify

\frac{5 θ}{5} : θ

\frac{5 θ}{5}

Divide the numbers:

\frac{5}{5} = 1

= θ

Simplify

5 arcsec (7) + 5 \cdot 2 πn : 5 arcsec (7) + 10 πn

5 arcsec (7) + 5 \cdot 2 πn

Multiply the numbers:

5 \cdot 2 = 10

= 5 arcsec (7) + 10 πn

θ = 5 arcsec (7) + 10 πn

θ = 5 arcsec (7) + 10 πn

θ = 5 arcsec (7) + 10 πn

Solve

\frac{θ}{5} = 2 π - arcsec (7) + 2 πn : θ = 10 π - 5 arcsec (7) + 10 πn

\frac{θ}{5} = 2 π - arcsec (7) + 2 πn

Multiply both sides by

5

\frac{θ}{5} = 2 π - arcsec (7) + 2 πn

Multiply both sides by

5

\frac{5 θ}{5} = 5 \cdot 2 π - 5 arcsec (7) + 5 \cdot 2 πn

Simplify

\frac{5 θ}{5} = 5 \cdot 2 π - 5 arcsec (7) + 5 \cdot 2 πn

Simplify

\frac{5 θ}{5} : θ

\frac{5 θ}{5}

Divide the numbers:

\frac{5}{5} = 1

= θ

Simplify

5 \cdot 2 π - 5 arcsec (7) + 5 \cdot 2 πn : 10 π - 5 arcsec (7) + 10 πn

5 \cdot 2 π - 5 arcsec (7) + 5 \cdot 2 πn

Multiply the numbers:

5 \cdot 2 = 10

= 10 π - 5 arcsec (7) + 10 πn

θ = 10 π - 5 arcsec (7) + 10 πn

θ = 10 π - 5 arcsec (7) + 10 πn

θ = 10 π - 5 arcsec (7) + 10 πn

θ = 5 arcsec (7) + 10 πn, θ = 10 π - 5 arcsec (7) + 10 πn

Show solutions in decimal form

θ = 5 \cdot 1.18319 \dots + 10 πn, θ = 10 π - 5 \cdot 1.18319 \dots + 10 πn

csc^{2} (x) + 2 cot (x) = 0

2 sin (x) tan (x) - tan (x) = 1 - 2 sin (x)

tan (θ) = \frac{2 3}{3} sin (θ)

tan (4 x) = - 1

3 (1 - cos (3 x)) = sin^{2} (3 x)

What is the general solution for sec(θ/5)=sqrt(7) ?
The general solution for sec(θ/5)=sqrt(7) is θ=5*1.18319…+10pin,θ=10pi-5*1.18319…+10pin