What is the general solution for 1609.3=(1.133^2)/((9.8)tan(θ)) ?

The general solution for 1609.3=(1.133^2)/((9.8)tan(θ)) is θ=0.00008…+pin

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Popular Trigonometry >

1609.3=(1.133^2)/((9.8)tan(θ))

Solution

1609.3 = \frac{1.13 3 ^{2}}{( 9.8 ) tan ( θ )}

Solution

θ = 0.00008 \dots + πn

Degrees

θ = 0.00466 \dots^{\circ} + 18 0^{\circ} n

Solution steps

1609.3 = \frac{1.13 3 ^{2}}{( 9.8 ) tan ( θ )}

Switch sides

\frac{1.13 3 ^{2}}{9.8 tan ( θ )} = 1609.3

Simplify

\frac{1.13 3 ^{2}}{9.8 tan ( θ )} : \frac{1.283689}{9.8 tan ( θ )}

\frac{1.13 3 ^{2}}{9.8 tan ( θ )}

1.13 3^{2} = 1.283689

= \frac{1.283689}{9.8 tan ( θ )}

\frac{1.283689}{9.8 tan ( θ )} = 1609.3

Multiply both sides by

tan (θ)

\frac{1.283689}{9.8 tan ( θ )} = 1609.3

Multiply both sides by

tan (θ)

\frac{1.283689}{9.8 tan ( θ )} tan (θ) = 1609.3 tan (θ)

Simplify

\frac{1.283689}{9.8} = 1609.3 tan (θ)

\frac{1.283689}{9.8} = 1609.3 tan (θ)

Switch sides

1609.3 tan (θ) = \frac{1.283689}{9.8}

Divide both sides by

1609.3

1609.3 tan (θ) = \frac{1.283689}{9.8}

Divide both sides by

1609.3

\frac{1609.3 tan ( θ )}{1609.3} = \frac{\frac{1.283689}{9.8}}{1609.3}

Simplify

\frac{1609.3 tan ( θ )}{1609.3} = \frac{\frac{1.283689}{9.8}}{1609.3}

Simplify

\frac{1609.3 tan ( θ )}{1609.3} : tan (θ)

\frac{1609.3 tan ( θ )}{1609.3}

Cancel the common factor:

1609.3

= tan (θ)

Simplify

\frac{\frac{1.283689}{9.8}}{1609.3} : \frac{1.283689}{15771.14}

\frac{\frac{1.283689}{9.8}}{1609.3}

Apply the fraction rule:

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

= \frac{1.283689}{9.8 \cdot 1609.3}

Multiply the numbers:

9.8 \cdot 1609.3 = 15771.14

= \frac{1.283689}{15771.14}

tan (θ) = \frac{1.283689}{15771.14}

tan (θ) = \frac{1.283689}{15771.14}

tan (θ) = \frac{1.283689}{15771.14}

Verify Solutions

Find undefined (singularity) points:

tan (θ) = 0

Take the denominator(s) of

\frac{1.13 3 ^{2}}{9.8 tan ( θ )}

and compare to zero

Solve

9.8 tan (θ) = 0 : tan (θ) = 0

9.8 tan (θ) = 0

Multiply both sides by

10

9.8 tan (θ) = 0

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

9.8 tan (θ) \cdot 10 = 0 \cdot 10

Refine

98 tan (θ) = 0

98 tan (θ) = 0

Divide both sides by

98

98 tan (θ) = 0

Divide both sides by

98

\frac{98 tan ( θ )}{98} = \frac{0}{98}

Simplify

tan (θ) = 0

tan (θ) = 0

The following points are undefined

tan (θ) = 0

Combine undefined points with solutions:

tan (θ) = \frac{1.283689}{15771.14}

Apply trig inverse properties

tan (θ) = \frac{1.283689}{15771.14}

General solutions for

tan (θ) = \frac{1.283689}{15771.14}

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

θ = arctan (\frac{1.283689}{15771.14}) + πn

θ = arctan (\frac{1.283689}{15771.14}) + πn

Show solutions in decimal form

θ = 0.00008 \dots + πn

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 1609.3=(1.133^2)/((9.8)tan(θ)) ?
The general solution for 1609.3=(1.133^2)/((9.8)tan(θ)) is θ=0.00008…+pin