What is the general solution for cos(θ)= 7/(3sqrt(17)) ?

The general solution for cos(θ)= 7/(3sqrt(17)) is θ=0.96925…+2pin,θ=2pi-0.96925…+2pin

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cos(θ)= 7/(3sqrt(17))

cos (θ) = \frac{7}{3 17}

θ = 0.96925 \dots + 2 πn, θ = 2 π - 0.96925 \dots + 2 πn

Radians

θ = 0.96925 \dots + 6.28318 \dots n, θ = 5.31393 \dots + 6.28318 \dots n

Solution steps

cos (θ) = \frac{7}{3 17}

Simplify

\frac{7}{3 17} : \frac{7 17}{51}

\frac{7}{3 17}

Multiply by the conjugate

\frac{17}{17}

= \frac{7 17}{3 17 17}

31717 = 51

31717

Apply radical rule:

a a = a

1717 = 17

= 3 \cdot 17

Multiply the numbers:

3 \cdot 17 = 51

= 51

= \frac{7 17}{51}

cos (θ) = \frac{7 17}{51}

Apply trig inverse properties

cos (θ) = \frac{7 17}{51}

General solutions for

cos (θ) = \frac{7 17}{51}

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

θ = arccos (\frac{7 17}{51}) + 2 πn, θ = 2 π - arccos (\frac{7 17}{51}) + 2 πn

θ = arccos (\frac{7 17}{51}) + 2 πn, θ = 2 π - arccos (\frac{7 17}{51}) + 2 πn

Show solutions in decimal form

θ = 0.96925 \dots + 2 πn, θ = 2 π - 0.96925 \dots + 2 πn

sin (A) - 0.1 \cdot cos (A) = \frac{6.94}{9.8}

t, s = 2 arctan (t)

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

cos (2 x) + 5 cos (x) = 3

sin (θ) = \frac{207.91 \cdot sin ( 31.7697 7 ^{\circ} )}{238.99}

What is the general solution for cos(θ)= 7/(3sqrt(17)) ?
The general solution for cos(θ)= 7/(3sqrt(17)) is θ=0.96925…+2pin,θ=2pi-0.96925…+2pin