What is the general solution for cos(a)=(-82)/(sqrt(140)*\sqrt{138)} ?

The general solution for cos(a)=(-82)/(sqrt(140)*\sqrt{138)} is a=2.20178…+2pin,a=-2.20178…+2pin

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Popular >

cos(a)=(-82)/(sqrt(140)*\sqrt{138)}

Solution

cos (a) = \frac{- 82}{140 \cdot 138}

Solution

a = 2.20178 \dots + 2 πn, a = - 2.20178 \dots + 2 πn

Radians

a = 2.20178 \dots + 6.28318 \dots n, a = - 2.20178 \dots + 6.28318 \dots n

Solution steps

cos (a) = \frac{- 82}{140 138}

Simplify

\frac{- 82}{140 138} : - \frac{41 4830}{4830}

\frac{- 82}{140 138}

Apply the fraction rule:

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

= - \frac{82}{140 138}

Cancel

\frac{82}{140 138} : \frac{41}{5 7 138}

\frac{82}{140 138}

Factor

82 : 2 \cdot 41

Factor

82 = 2 \cdot 41

Factor

140 : 257

Factor

140 = 2^{2} \cdot 5 \cdot 7

= 2^{2} \cdot 5 \cdot 7

Apply radical rule:

= 57 2^{2}

Simplify

2^{2} : 2

2^{2}

Apply radical rule:

assuming

a \geq 0

= 2

= 257

= \frac{2 \cdot 41}{2 5 7 138}

Divide the numbers:

\frac{2}{2} = 1

= \frac{41}{5 7 138}

= - \frac{41}{5 7 138}

Simplify

57138 : 4830

57138

Apply radical rule:

a b = a \cdot b

57138 = 5 \cdot 7 \cdot 138

= 5 \cdot 7 \cdot 138

Multiply the numbers:

5 \cdot 7 \cdot 138 = 4830

= 4830

= - \frac{41}{4830}

Rationalize

- \frac{41}{4830} : - \frac{41 4830}{4830}

- \frac{41}{4830}

Multiply by the conjugate

\frac{4830}{4830}

= - \frac{41 4830}{4830 4830}

48304830 = 4830

48304830

Apply radical rule:

a a = a

48304830 = 4830

= 4830

= - \frac{41 4830}{4830}

= - \frac{41 4830}{4830}

cos (a) = - \frac{41 4830}{4830}

Apply trig inverse properties

cos (a) = - \frac{41 4830}{4830}

General solutions for

cos (a) = - \frac{41 4830}{4830}

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

a = arccos (- \frac{41 4830}{4830}) + 2 πn, a = - arccos (- \frac{41 4830}{4830}) + 2 πn

a = arccos (- \frac{41 4830}{4830}) + 2 πn, a = - arccos (- \frac{41 4830}{4830}) + 2 πn

Show solutions in decimal form

a = 2.20178 \dots + 2 πn, a = - 2.20178 \dots + 2 πn

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Frequently Asked Questions (FAQ)

What is the general solution for cos(a)=(-82)/(sqrt(140)*\sqrt{138)} ?
The general solution for cos(a)=(-82)/(sqrt(140)*\sqrt{138)} is a=2.20178…+2pin,a=-2.20178…+2pin