What is the general solution for cos(x)= 6/(7sqrt(76)) ?

The general solution for cos(x)= 6/(7sqrt(76)) is x=1.47231…+2pin,x=2pi-1.47231…+2pin

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cos(x)= 6/(7sqrt(76))

cos (x) = \frac{6}{7 76}

x = 1.47231 \dots + 2 πn, x = 2 π - 1.47231 \dots + 2 πn

Radians

x = 1.47231 \dots + 6.28318 \dots n, x = 4.81086 \dots + 6.28318 \dots n

Solution steps

cos (x) = \frac{6}{7 76}

Simplify

\frac{6}{7 76} : \frac{3 19}{133}

\frac{6}{7 76}

Factor

6 : 2 \cdot 3

Factor

6 = 2 \cdot 3

Factor

76 : 219

Factor

76 = 2^{2} \cdot 19

= 2^{2} \cdot 19

Apply radical rule:

= 19 2^{2}

Simplify

2^{2} : 2

2^{2}

Apply radical rule:

assuming

a \geq 0

= 2

= 219

= \frac{2 \cdot 3}{7 \cdot 2 19}

Divide the numbers:

\frac{2}{2} = 1

= \frac{3}{7 19}

Rationalize

\frac{3}{7 19} : \frac{3 19}{133}

\frac{3}{7 19}

Multiply by the conjugate

\frac{19}{19}

= \frac{3 19}{7 19 19}

71919 = 133

71919

Apply radical rule:

a a = a

1919 = 19

= 7 \cdot 19

Multiply the numbers:

7 \cdot 19 = 133

= 133

= \frac{3 19}{133}

= \frac{3 19}{133}

cos (x) = \frac{3 19}{133}

Apply trig inverse properties

cos (x) = \frac{3 19}{133}

General solutions for

cos (x) = \frac{3 19}{133}

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

x = arccos (\frac{3 19}{133}) + 2 πn, x = 2 π - arccos (\frac{3 19}{133}) + 2 πn

x = arccos (\frac{3 19}{133}) + 2 πn, x = 2 π - arccos (\frac{3 19}{133}) + 2 πn

Show solutions in decimal form

x = 1.47231 \dots + 2 πn, x = 2 π - 1.47231 \dots + 2 πn

2 sin (φ) - 1 = 0

sin (x - 2 0^{\circ}) = cos (x)

x, z = sin^{2} (x - 2 π y)

sin (θ) = \frac{3}{3 5}

6 cos (θ) sin (θ) + cos (θ) = 0

What is the general solution for cos(x)= 6/(7sqrt(76)) ?
The general solution for cos(x)= 6/(7sqrt(76)) is x=1.47231…+2pin,x=2pi-1.47231…+2pin