What is the general solution for solvefor g,θ=arctan((5.54)/(10g)+0.2) ?

The general solution for solvefor g,θ=arctan((5.54)/(10g)+0.2) is g=(5.54)/(10(tan(θ)-0.2))

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Popular >

solvefor g,θ=arctan((5.54)/(10g)+0.2)

Solution

solve for

g, θ = arctan (\frac{5.54}{10 g} + 0.2)

Solution

g = \frac{5.54}{10 ( tan ( θ ) - 0.2 )}

Solution steps

θ = arctan (\frac{5.54}{10 g} + 0.2)

Switch sides

arctan (\frac{5.54}{10 g} + 0.2) = θ

Apply trig inverse properties

arctan (\frac{5.54}{10 g} + 0.2) = θ

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

\frac{5.54}{10 g} + 0.2 = tan (θ)

\frac{5.54}{10 g} + 0.2 = tan (θ)

Solve

\frac{5.54}{10 g} + 0.2 = tan (θ) : g = \frac{5.54}{10 ( tan ( θ ) - 0.2 )}; θ \neq = 0.19739 \dots + πn

\frac{5.54}{10 g} + 0.2 = tan (θ)

Move

0.2

to the right side

\frac{5.54}{10 g} + 0.2 = tan (θ)

Subtract

0.2

from both sides

\frac{5.54}{10 g} + 0.2 - 0.2 = tan (θ) - 0.2

Simplify

\frac{5.54}{10 g} = tan (θ) - 0.2

\frac{5.54}{10 g} = tan (θ) - 0.2

Multiply both sides by

g

\frac{5.54}{10 g} = tan (θ) - 0.2

Multiply both sides by

g

\frac{5.54}{10 g} g = tan (θ) g - 0.2 g

Simplify

\frac{5.54}{10} = tan (θ) g - 0.2 g

\frac{5.54}{10} = tan (θ) g - 0.2 g

Switch sides

tan (θ) g - 0.2 g = \frac{5.54}{10}

Factor

tan (θ) g - 0.2 g : g (tan (θ) - 0.2)

tan (θ) g - 0.2 g

Factor out common term

g

= g (tan (θ) - 0.2)

g (tan (θ) - 0.2) = \frac{5.54}{10}

Divide both sides by

tan (θ) - 0.2; θ \neq = 0.19739 \dots + πn

g (tan (θ) - 0.2) = \frac{5.54}{10}

Divide both sides by

tan (θ) - 0.2; θ \neq = 0.19739 \dots + πn

\frac{g ( tan ( θ ) - 0.2 )}{tan ( θ ) - 0.2} = \frac{\frac{5.54}{10}}{tan ( θ ) - 0.2}; θ \neq = 0.19739 \dots + πn

Simplify

\frac{g ( tan ( θ ) - 0.2 )}{tan ( θ ) - 0.2} = \frac{\frac{5.54}{10}}{tan ( θ ) - 0.2}

Simplify

\frac{g ( tan ( θ ) - 0.2 )}{tan ( θ ) - 0.2} : g

\frac{g ( tan ( θ ) - 0.2 )}{tan ( θ ) - 0.2}

Cancel the common factor:

tan (θ) - 0.2

= g

Simplify

\frac{\frac{5.54}{10}}{tan ( θ ) - 0.2} : \frac{5.54}{10 ( tan ( θ ) - 0.2 )}

\frac{\frac{5.54}{10}}{tan ( θ ) - 0.2}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{5.54}{10 ( tan ( θ ) - 0.2 )}

g = \frac{5.54}{10 ( tan ( θ ) - 0.2 )}; θ \neq = 0.19739 \dots + πn

g = \frac{5.54}{10 ( tan ( θ ) - 0.2 )}; θ \neq = 0.19739 \dots + πn

g = \frac{5.54}{10 ( tan ( θ ) - 0.2 )}; θ \neq = 0.19739 \dots + πn

g = \frac{5.54}{10 ( tan ( θ ) - 0.2 )}

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Frequently Asked Questions (FAQ)

What is the general solution for solvefor g,θ=arctan((5.54)/(10g)+0.2) ?
The general solution for solvefor g,θ=arctan((5.54)/(10g)+0.2) is g=(5.54)/(10(tan(θ)-0.2))