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

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

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cos(x)= 4/(sqrt(3.38^2+4^2))

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

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

Radians

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

Solution steps

cos (x) = \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 (x) = \frac{4 27.4244}{27.4244}

Apply trig inverse properties

cos (x) = \frac{4 27.4244}{27.4244}

General solutions for

cos (x) = \frac{4 27.4244}{27.4244}

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

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

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

Show solutions in decimal form

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

x, y = \frac{1}{π} arctan (\frac{x}{s}) + \frac{1}{2}

tan^{2} (θ) + 8 tan (θ) + 6 = 0

3 - sin (θ) = 5 sin (θ)

sin (x) + sin (2 x) = 0, 0 \leq x \leq 2 π

8 sin (2 x) = 16 cos (x)

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