What is the general solution for sqrt((-(\sqrt{2))/3)^2+1}=sec(θ) ?

The general solution for sqrt((-(\sqrt{2))/3)^2+1}=sec(θ) is θ=0.44051…+2pin,θ=2pi-0.44051…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sqrt((-(\sqrt{2))/3)^2+1}=sec(θ)

Solution

(- \frac{2}{3})^{2} + 1 = sec (θ)

Solution

θ = 0.44051 \dots + 2 πn, θ = 2 π - 0.44051 \dots + 2 πn

Degrees

θ = 25.23940 \dots^{\circ} + 36 0^{\circ} n, θ = 334.76059 \dots^{\circ} + 36 0^{\circ} n

Solution steps

(- \frac{2}{3})^{2} + 1 = sec (θ)

Switch sides

sec (θ) = (- \frac{2}{3})^{2} + 1

Simplify

(- \frac{2}{3})^{2} + 1 : \frac{11}{3}

(- \frac{2}{3})^{2} + 1

(- \frac{2}{3})^{2} = \frac{2}{3 ^{2}}

(- \frac{2}{3})^{2}

Apply exponent rule:

(- a)^{n} = a^{n},

n

is even

(- \frac{2}{3})^{2} = (\frac{2}{3})^{2}

= (\frac{2}{3})^{2}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( 2 ) ^{2}}{3 ^{2}}

(2)^{2} : 2

Apply radical rule:

a = a^{\frac{1}{2}}

= (2^{\frac{1}{2}})^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 2^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

Multiply fractions:

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

= \frac{1 \cdot 2}{2}

Cancel the common factor:

2

= 1

= 2

= \frac{2}{3 ^{2}}

= \frac{2}{3 ^{2}} + 1

3^{2} = 9

= \frac{2}{9} + 1

Join

\frac{2}{9} + 1 : \frac{11}{9}

\frac{2}{9} + 1

Convert element to fraction:

1 = \frac{1 \cdot 9}{9}

= \frac{1 \cdot 9}{9} + \frac{2}{9}

Since the denominators are equal, combine the fractions:

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

= \frac{1 \cdot 9 + 2}{9}

1 \cdot 9 + 2 = 11

1 \cdot 9 + 2

Multiply the numbers:

1 \cdot 9 = 9

= 9 + 2

Add the numbers:

9 + 2 = 11

= 11

= \frac{11}{9}

= \frac{11}{9}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{11}{9}

9 = 3

9

Factor the number:

9 = 3^{2}

= 3^{2}

Apply radical rule:

3^{2} = 3

= 3

= \frac{11}{3}

sec (θ) = \frac{11}{3}

Apply trig inverse properties

sec (θ) = \frac{11}{3}

General solutions for

sec (θ) = \frac{11}{3}

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

θ = arcsec (\frac{11}{3}) + 2 πn, θ = 2 π - arcsec (\frac{11}{3}) + 2 πn

θ = arcsec (\frac{11}{3}) + 2 πn, θ = 2 π - arcsec (\frac{11}{3}) + 2 πn

Show solutions in decimal form

θ = 0.44051 \dots + 2 πn, θ = 2 π - 0.44051 \dots + 2 πn

Popular Examples

1=sech^2(x)

1 = sech^{2} (x)

tan(θ)=0.86667

tan (θ) = 0.86667

sin(x)*cos^2(x)=1

sin (x) \cdot cos^{2} (x) = 1

solvefor t,fw=2+cos(10pit)solve for

t, f w = 2 + cos (10 π t)

tan(θ)-sec(θ)=sqrt(3)

tan (θ) - sec (θ) = 3

Frequently Asked Questions (FAQ)

What is the general solution for sqrt((-(\sqrt{2))/3)^2+1}=sec(θ) ?
The general solution for sqrt((-(\sqrt{2))/3)^2+1}=sec(θ) is θ=0.44051…+2pin,θ=2pi-0.44051…+2pin