What is the general solution for cos(x)=(11)/(sqrt(17*38)) ?

The general solution for cos(x)=(11)/(sqrt(17*38)) is x=1.12321…+2pin,x=2pi-1.12321…+2pin

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cos(x)=(11)/(sqrt(17*38))

cos (x) = \frac{11}{17 \cdot 38}

x = 1.12321 \dots + 2 πn, x = 2 π - 1.12321 \dots + 2 πn

Radians

x = 1.12321 \dots + 6.28318 \dots n, x = 5.15997 \dots + 6.28318 \dots n

Solution steps

cos (x) = \frac{11}{17 \cdot 38}

Simplify

\frac{11}{17 \cdot 38} : \frac{11 646}{646}

\frac{11}{17 \cdot 38}

Multiply the numbers:

17 \cdot 38 = 646

= \frac{11}{646}

Rationalize

\frac{11}{646} : \frac{11 646}{646}

\frac{11}{646}

Multiply by the conjugate

\frac{646}{646}

= \frac{11 646}{646 646}

646646 = 646

646646

Apply radical rule:

a a = a

646646 = 646

= 646

= \frac{11 646}{646}

= \frac{11 646}{646}

cos (x) = \frac{11 646}{646}

Apply trig inverse properties

cos (x) = \frac{11 646}{646}

General solutions for

cos (x) = \frac{11 646}{646}

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

x = arccos (\frac{11 646}{646}) + 2 πn, x = 2 π - arccos (\frac{11 646}{646}) + 2 πn

x = arccos (\frac{11 646}{646}) + 2 πn, x = 2 π - arccos (\frac{11 646}{646}) + 2 πn

Show solutions in decimal form

x = 1.12321 \dots + 2 πn, x = 2 π - 1.12321 \dots + 2 πn

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sin (x) tan (x) + 3 sin (x) = 0

4 = 5 + 3 sin (2 t - \frac{π}{5})

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

tan (θ) = - 0.5586, 0 \leq θ < 2 π

What is the general solution for cos(x)=(11)/(sqrt(17*38)) ?
The general solution for cos(x)=(11)/(sqrt(17*38)) is x=1.12321…+2pin,x=2pi-1.12321…+2pin