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

The general solution for cos(θ)= 4/(sqrt(3.38^2+2^2)) is No Solution for θ\in\mathbb{R}

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cos(θ)= 4/(sqrt(3.38^2+2^2))

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

No Solution for θ \in R

Solution steps

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

Simplify

\frac{4}{3.3 8 ^{2} + 2 ^{2}} : \frac{4 15.4244}{15.4244}

\frac{4}{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{4}{15.4244}

Rationalize

\frac{4}{15.4244} : \frac{4 15.4244}{15.4244}

\frac{4}{15.4244}

Multiply by the conjugate

\frac{15.4244}{15.4244}

= \frac{4 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{4 15.4244}{15.4244}

= \frac{4 15.4244}{15.4244}

cos (θ) = \frac{4 15.4244}{15.4244}

- 1 \leq cos (x) \leq 1

No Solution for θ \in R

23 sin (2 θ) = 3

0 = 3 - 2 sin (x)

- 2 sin^{2} (θ) + cos (θ) = - 1

4 cos (θ) = 4 (1 - cos (θ))

2 cos (x) = 1.7

What is the general solution for cos(θ)= 4/(sqrt(3.38^2+2^2)) ?
The general solution for cos(θ)= 4/(sqrt(3.38^2+2^2)) is No Solution for θ\in\mathbb{R}