What is the general solution for cos(θ)= 4/(sqrt(3.38^2+4^2)) ?

The general solution for cos(θ)= 4/(sqrt(3.38^2+4^2)) is θ=0.70158…+2pin,θ=2pi-0.70158…+2pin

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cos(θ)= 4/(sqrt(3.38^2+4^2))

cos (θ) = \frac{4}{3.3 8 ^{2} + 4 ^{2}}

θ = 0.70158 \dots + 2 πn, θ = 2 π - 0.70158 \dots + 2 πn

Radians

θ = 0.70158 \dots + 6.28318 \dots n, θ = 5.58160 \dots + 6.28318 \dots n

Solution steps

cos (θ) = \frac{4}{3.3 8 ^{2} + 4 ^{2}}

Simplify

\frac{4}{3.3 8 ^{2} + 4 ^{2}} : \frac{4 27.4244}{27.4244}

\frac{4}{3.3 8 ^{2} + 4 ^{2}}

3.3 8^{2} + 4^{2} = 27.4244

3.3 8^{2} + 4^{2}

3.3 8^{2} = 11.4244

= 11.4244 + 4^{2}

4^{2} = 16

= 11.4244 + 16

Add the numbers:

11.4244 + 16 = 27.4244

= 27.4244

= \frac{4}{27.4244}

Rationalize

\frac{4}{27.4244} : \frac{4 27.4244}{27.4244}

\frac{4}{27.4244}

Multiply by the conjugate

\frac{27.4244}{27.4244}

= \frac{4 27.4244}{27.4244 27.4244}

27.4244 27.4244 = 27.4244

27.4244 27.4244

Apply radical rule:

a a = a

27.4244 27.4244 = 27.4244

= 27.4244

= \frac{4 27.4244}{27.4244}

= \frac{4 27.4244}{27.4244}

cos (θ) = \frac{4 27.4244}{27.4244}

Apply trig inverse properties

cos (θ) = \frac{4 27.4244}{27.4244}

General solutions for

cos (θ) = \frac{4 27.4244}{27.4244}

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

θ = arccos (\frac{4 27.4244}{27.4244}) + 2 πn, θ = 2 π - arccos (\frac{4 27.4244}{27.4244}) + 2 πn

θ = arccos (\frac{4 27.4244}{27.4244}) + 2 πn, θ = 2 π - arccos (\frac{4 27.4244}{27.4244}) + 2 πn

Show solutions in decimal form

θ = 0.70158 \dots + 2 πn, θ = 2 π - 0.70158 \dots + 2 πn

tan (x - 1 0^{\circ}) = - 0.1

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

4 cos (3 x) - 1 = 2 sin (3 x) tan (3 x)

tan (θ) = \frac{15}{20}

- cos (x) = 0.9

What is the general solution for cos(θ)= 4/(sqrt(3.38^2+4^2)) ?
The general solution for cos(θ)= 4/(sqrt(3.38^2+4^2)) is θ=0.70158…+2pin,θ=2pi-0.70158…+2pin