What is the general solution for cos(x)= 6/(sqrt(61)) ?

The general solution for cos(x)= 6/(sqrt(61)) is x=0.69473…+2pin,x=2pi-0.69473…+2pin

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cos(x)= 6/(sqrt(61))

cos (x) = \frac{6}{61}

x = 0.69473 \dots + 2 πn, x = 2 π - 0.69473 \dots + 2 πn

Radians

x = 0.69473 \dots + 6.28318 \dots n, x = 5.58844 \dots + 6.28318 \dots n

Solution steps

cos (x) = \frac{6}{61}

Simplify

\frac{6}{61} : \frac{6 61}{61}

\frac{6}{61}

Multiply by the conjugate

\frac{61}{61}

= \frac{6 61}{61 61}

6161 = 61

6161

Apply radical rule:

a a = a

6161 = 61

= 61

= \frac{6 61}{61}

cos (x) = \frac{6 61}{61}

Apply trig inverse properties

cos (x) = \frac{6 61}{61}

General solutions for

cos (x) = \frac{6 61}{61}

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

x = arccos (\frac{6 61}{61}) + 2 πn, x = 2 π - arccos (\frac{6 61}{61}) + 2 πn

x = arccos (\frac{6 61}{61}) + 2 πn, x = 2 π - arccos (\frac{6 61}{61}) + 2 πn

Show solutions in decimal form

x = 0.69473 \dots + 2 πn, x = 2 π - 0.69473 \dots + 2 πn

sin (a + 3 0^{\circ}) = - \frac{3}{2}

cos (2 a) = 1

cos (\frac{2}{3} x) = 0

sin (2 x) cos (2 x) = 2

\frac{cos ( t )}{3 cos ( 3 t )} = 0

What is the general solution for cos(x)= 6/(sqrt(61)) ?
The general solution for cos(x)= 6/(sqrt(61)) is x=0.69473…+2pin,x=2pi-0.69473…+2pin