What is the general solution for cos(θ)= 4/(sqrt(17)) ?

The general solution for cos(θ)= 4/(sqrt(17)) is θ=0.24497…+2pin,θ=2pi-0.24497…+2pin

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cos(θ)= 4/(sqrt(17))

cos (θ) = \frac{4}{17}

θ = 0.24497 \dots + 2 πn, θ = 2 π - 0.24497 \dots + 2 πn

Radians

θ = 0.24497 \dots + 6.28318 \dots n, θ = 6.03820 \dots + 6.28318 \dots n

Solution steps

cos (θ) = \frac{4}{17}

Simplify

\frac{4}{17} : \frac{4 17}{17}

\frac{4}{17}

Multiply by the conjugate

\frac{17}{17}

= \frac{4 17}{17 17}

1717 = 17

1717

Apply radical rule:

a a = a

1717 = 17

= 17

= \frac{4 17}{17}

cos (θ) = \frac{4 17}{17}

Apply trig inverse properties

cos (θ) = \frac{4 17}{17}

General solutions for

cos (θ) = \frac{4 17}{17}

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

θ = arccos (\frac{4 17}{17}) + 2 πn, θ = 2 π - arccos (\frac{4 17}{17}) + 2 πn

θ = arccos (\frac{4 17}{17}) + 2 πn, θ = 2 π - arccos (\frac{4 17}{17}) + 2 πn

Show solutions in decimal form

θ = 0.24497 \dots + 2 πn, θ = 2 π - 0.24497 \dots + 2 πn

- csc^{2} (x) + 2 csc (x) cot (x) = 0

6 sin (A) + 3 = 4 sin (A) + 4

a, - 10 = sin (a) + 15.2 cos (a)

0 = - 6 sin^{2} (θ) + 3 sin (θ) + 2

sin (2 x + \frac{3}{π}) = \frac{1}{2}

What is the general solution for cos(θ)= 4/(sqrt(17)) ?
The general solution for cos(θ)= 4/(sqrt(17)) is θ=0.24497…+2pin,θ=2pi-0.24497…+2pin