What is the general solution for tan(θ)=(sqrt(48))/8 ?

The general solution for tan(θ)=(sqrt(48))/8 is θ=0.71372…+pin

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tan(θ)=(sqrt(48))/8

tan (θ) = \frac{48}{8}

θ = 0.71372 \dots + πn

Solution steps

tan (θ) = \frac{48}{8}

Simplify

\frac{48}{8} : \frac{3}{2}

\frac{48}{8}

Factor

48 : 2^{2} 3

Factor

48 = 2^{4} \cdot 3

= 2^{4} \cdot 3

Apply radical rule:

= 3 2^{4}

Simplify

2^{4} : 2^{2}

2^{4}

Apply exponent rule:

a^{b c} = (a^{b})^{c}

2^{4} = 2^{2 \cdot 2} = (2^{2})^{2}

= (2^{2})^{2}

Apply radical rule:

assuming

a \geq 0

= 2^{2}

= 2^{2} 3

Factor

8 : 2^{3}

Factor

8 = 2^{3}

= \frac{2 ^{2} 3}{2 ^{3}}

Cancel

\frac{2 ^{2} 3}{2 ^{3}} : \frac{3}{2}

\frac{2 ^{2} 3}{2 ^{3}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{2 ^{2}}{2 ^{3}} = \frac{1}{2 ^{3 - 2}}

= \frac{3}{2 ^{3 - 2}}

Subtract the numbers:

3 - 2 = 1

= \frac{3}{2}

= \frac{3}{2}

tan (θ) = \frac{3}{2}

Apply trig inverse properties

tan (θ) = \frac{3}{2}

General solutions for

tan (θ) = \frac{3}{2}

tan (x) = a \Rightarrow x = arctan (a) + πn

θ = arctan (\frac{3}{2}) + πn

θ = arctan (\frac{3}{2}) + πn

Show solutions in decimal form

θ = 0.71372 \dots + πn

- 2 cos (2 x) = 2 sin (x)

sin (θ) - 0.2 cos (θ) = \frac{7.51}{9.8}

23 = - 6 tan (θ)

- 3 - \frac{5}{2} \cdot cos (θ) = - 3 - 3 cos (θ)

tan (θ) = - \frac{6}{5}

What is the general solution for tan(θ)=(sqrt(48))/8 ?
The general solution for tan(θ)=(sqrt(48))/8 is θ=0.71372…+pin