What is the general solution for cos(θ)=(-18)/(sqrt(20)*\sqrt{26)} ?

The general solution for cos(θ)=(-18)/(sqrt(20)*\sqrt{26)} is θ=2.48054…+2pin,θ=-2.48054…+2pin

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Popular >

cos(θ)=(-18)/(sqrt(20)*\sqrt{26)}

Solution

cos (θ) = \frac{- 18}{20 \cdot 26}

Solution

θ = 2.48054 \dots + 2 πn, θ = - 2.48054 \dots + 2 πn

Radians

θ = 2.48054 \dots + 6.28318 \dots n, θ = - 2.48054 \dots + 6.28318 \dots n

Solution steps

cos (θ) = \frac{- 18}{20 26}

Simplify

\frac{- 18}{20 26} : - \frac{9 130}{130}

\frac{- 18}{20 26}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{18}{20 26}

Cancel

\frac{18}{20 26} : \frac{3 ^{2}}{5 26}

\frac{18}{20 26}

Factor

18 : 3^{2} \cdot 2

Factor

18 = 3^{2} \cdot 2

Factor

20 : 25

Factor

20 = 2^{2} \cdot 5

= 2^{2} \cdot 5

Apply radical rule:

= 5 2^{2}

Simplify

2^{2} : 2

2^{2}

Apply radical rule:

assuming

a \geq 0

= 2

= 25

= \frac{3 ^{2} \cdot 2}{2 5 26}

Divide the numbers:

\frac{2}{2} = 1

= \frac{3 ^{2}}{5 26}

= - \frac{3 ^{2}}{5 26}

Simplify

526 : 130

526

Apply radical rule:

a b = a \cdot b

526 = 5 \cdot 26

= 5 \cdot 26

Multiply the numbers:

5 \cdot 26 = 130

= 130

= - \frac{3 ^{2}}{130}

3^{2} = 9

= - \frac{9}{130}

Rationalize

- \frac{9}{130} : - \frac{9 130}{130}

- \frac{9}{130}

Multiply by the conjugate

\frac{130}{130}

= - \frac{9 130}{130 130}

130130 = 130

130130

Apply radical rule:

a a = a

130130 = 130

= 130

= - \frac{9 130}{130}

= - \frac{9 130}{130}

cos (θ) = - \frac{9 130}{130}

Apply trig inverse properties

cos (θ) = - \frac{9 130}{130}

General solutions for

cos (θ) = - \frac{9 130}{130}

cos (x) = - a \Rightarrow x = arccos (- a) + 2 πn, x = - arccos (- a) + 2 πn

θ = arccos (- \frac{9 130}{130}) + 2 πn, θ = - arccos (- \frac{9 130}{130}) + 2 πn

θ = arccos (- \frac{9 130}{130}) + 2 πn, θ = - arccos (- \frac{9 130}{130}) + 2 πn

Show solutions in decimal form

θ = 2.48054 \dots + 2 πn, θ = - 2.48054 \dots + 2 πn

Popular Examples

sin(2x)=-cos(x),0<= x<= 2pi

sin (2 x) = - cos (x), 0 \leq x \leq 2 π

sin(θ)=(5pi)/6

sin (θ) = \frac{5 π}{6}

sin(x)=(4.2)/(9.9)

sin (x) = \frac{4.2}{9.9}

sin(x)-0.5cos(x)=0.1

sin (x) - 0.5 cos (x) = 0.1

cot(θ)=0.8701

cot (θ) = 0.8701

Frequently Asked Questions (FAQ)

What is the general solution for cos(θ)=(-18)/(sqrt(20)*\sqrt{26)} ?
The general solution for cos(θ)=(-18)/(sqrt(20)*\sqrt{26)} is θ=2.48054…+2pin,θ=-2.48054…+2pin