What is the general solution for solvefor y,d=arctan((10)/(y/(67)*1000)) ?

The general solution for solvefor y,d=arctan((10)/(y/(67)*1000)) is y=(67)/(100tan(d))

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solvefor y,d=arctan((10)/(y/(67)*1000))

solve for

y, d = arctan (\frac{10}{\frac{y}{67} \cdot 1000})

y = \frac{67}{100 tan ( d )}

Solution steps

d = arctan (\frac{10}{\frac{y}{67} \cdot 1000})

Switch sides

arctan (\frac{10}{\frac{y}{67} \cdot 1000}) = d

Apply trig inverse properties

arctan (\frac{10}{\frac{y}{67} \cdot 1000}) = d

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

\frac{10}{\frac{y}{67} \cdot 1000} = tan (d)

\frac{10}{\frac{y}{67} \cdot 1000} = tan (d)

Solve

\frac{10}{\frac{y}{67} \cdot 1000} = tan (d) : y = \frac{67}{100 tan ( d )}; d \neq = πn

\frac{10}{\frac{y}{67} \cdot 1000} = tan (d)

Simplify

\frac{10}{\frac{y}{67} \cdot 1000} : \frac{67}{100 y}

\frac{10}{\frac{y}{67} \cdot 1000}

Multiply

\frac{y}{67} \cdot 1000 : \frac{1000 y}{67}

\frac{y}{67} \cdot 1000

Multiply fractions:

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

= \frac{y \cdot 1000}{67}

= \frac{10}{\frac{1000 y}{67}}

Apply the fraction rule:

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

= \frac{10 \cdot 67}{y \cdot 1000}

Multiply the numbers:

10 \cdot 67 = 670

= \frac{670}{1000 y}

Cancel the common factor:

10

= \frac{67}{100 y}

\frac{67}{100 y} = tan (d)

Multiply both sides by

y

\frac{67}{100 y} = tan (d)

Multiply both sides by

y

\frac{67}{100 y} y = tan (d) y

Simplify

\frac{67}{100} = tan (d) y

\frac{67}{100} = tan (d) y

Switch sides

tan (d) y = \frac{67}{100}

Divide both sides by

tan (d); d \neq = πn

tan (d) y = \frac{67}{100}

Divide both sides by

tan (d); d \neq = πn

\frac{tan ( d ) y}{tan ( d )} = \frac{\frac{67}{100}}{tan ( d )}; d \neq = πn

Simplify

\frac{tan ( d ) y}{tan ( d )} = \frac{\frac{67}{100}}{tan ( d )}

Simplify

\frac{tan ( d ) y}{tan ( d )} : y

\frac{tan ( d ) y}{tan ( d )}

Cancel the common factor:

tan (d)

= y

Simplify

\frac{\frac{67}{100}}{tan ( d )} : \frac{67}{100 tan ( d )}

\frac{\frac{67}{100}}{tan ( d )}

Apply the fraction rule:

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

= \frac{67}{100 tan ( d )}

y = \frac{67}{100 tan ( d )}; d \neq = πn

y = \frac{67}{100 tan ( d )}; d \neq = πn

y = \frac{67}{100 tan ( d )}; d \neq = πn

y = \frac{67}{100 tan ( d )}

2 arccos (x) = π

- 2 cos (θ) + 1 = 5 cos (θ) + 0

2 sin^{2} (θ) - sin (θ) = 0, 0 \leq θ < 2 π

cos (x^{2}) = \frac{1}{2}

sec^{2} (x) - 7 sec (x) = 0

What is the general solution for solvefor y,d=arctan((10)/(y/(67)*1000)) ?
The general solution for solvefor y,d=arctan((10)/(y/(67)*1000)) is y=(67)/(100tan(d))