What is the general solution for cos(θ)= 2/(sqrt(3.38^2+2^2)) ?

The general solution for cos(θ)= 2/(sqrt(3.38^2+2^2)) is θ=1.03649…+2pin,θ=2pi-1.03649…+2pin

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cos(θ)= 2/(sqrt(3.38^2+2^2))

cos (θ) = \frac{2}{3.3 8 ^{2} + 2 ^{2}}

θ = 1.03649 \dots + 2 πn, θ = 2 π - 1.03649 \dots + 2 πn

Radians

θ = 1.03649 \dots + 6.28318 \dots n, θ = 5.24669 \dots + 6.28318 \dots n

Solution steps

cos (θ) = \frac{2}{3.3 8 ^{2} + 2 ^{2}}

Simplify

\frac{2}{3.3 8 ^{2} + 2 ^{2}} : \frac{2 15.4244}{15.4244}

\frac{2}{3.3 8 ^{2} + 2 ^{2}}

3.3 8^{2} + 2^{2} = 15.4244

3.3 8^{2} + 2^{2}

3.3 8^{2} = 11.4244

= 11.4244 + 2^{2}

2^{2} = 4

= 11.4244 + 4

Add the numbers:

11.4244 + 4 = 15.4244

= 15.4244

= \frac{2}{15.4244}

Rationalize

\frac{2}{15.4244} : \frac{2 15.4244}{15.4244}

\frac{2}{15.4244}

Multiply by the conjugate

\frac{15.4244}{15.4244}

= \frac{2 15.4244}{15.4244 15.4244}

15.4244 15.4244 = 15.4244

15.4244 15.4244

Apply radical rule:

a a = a

15.4244 15.4244 = 15.4244

= 15.4244

= \frac{2 15.4244}{15.4244}

= \frac{2 15.4244}{15.4244}

cos (θ) = \frac{2 15.4244}{15.4244}

Apply trig inverse properties

cos (θ) = \frac{2 15.4244}{15.4244}

General solutions for

cos (θ) = \frac{2 15.4244}{15.4244}

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

θ = arccos (\frac{2 15.4244}{15.4244}) + 2 πn, θ = 2 π - arccos (\frac{2 15.4244}{15.4244}) + 2 πn

θ = arccos (\frac{2 15.4244}{15.4244}) + 2 πn, θ = 2 π - arccos (\frac{2 15.4244}{15.4244}) + 2 πn

Show solutions in decimal form

θ = 1.03649 \dots + 2 πn, θ = 2 π - 1.03649 \dots + 2 πn

3 tan (θ) - cot (θ) = 5

cos (x) \cdot sin (x) = 1

3 tan^{2} (θ) + 2 tan (θ) - 3 = 0

sinh (x) = \frac{1}{2}

sin^{2} (x) \cdot sec (x) = \frac{sin ^{2} ( x )}{cot ( x )}

What is the general solution for cos(θ)= 2/(sqrt(3.38^2+2^2)) ?
The general solution for cos(θ)= 2/(sqrt(3.38^2+2^2)) is θ=1.03649…+2pin,θ=2pi-1.03649…+2pin