What is the general solution for tan(θ+26.565)=(12.5^2)/(9.81(60)) ?

The general solution for tan(θ+26.565)=(12.5^2)/(9.81(60)) is θ=0.25947…+180n-26.56500…

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tan(θ+26.565)=(12.5^2)/(9.81(60))

tan (θ + 26.56 5^{\circ}) = \frac{12. 5 ^{2}}{9.81 ( 60 )}

θ = 0.25947 \dots + 18 0^{\circ} n - 26.56500 \dots^{\circ}

Radians

θ = 0.25947 \dots - \frac{571 π}{3869} + πn

Solution steps

tan (θ + 26.56 5^{\circ}) = \frac{12. 5 ^{2}}{9.81 ( 60 )}

Simplify

\frac{12. 5 ^{2}}{9.81 \cdot 60} : \frac{156.25}{588.6}

\frac{12. 5 ^{2}}{9.81 \cdot 60}

Multiply the numbers:

9.81 \cdot 60 = 588.6

= \frac{12. 5 ^{2}}{588.6}

12. 5^{2} = 156.25

= \frac{156.25}{588.6}

Apply trig inverse properties

tan (θ + 26.56500 \dots^{\circ}) = \frac{156.25}{588.6}

General solutions for

tan (θ + 26.56500 \dots^{\circ}) = \frac{156.25}{588.6}

tan (x) = a \Rightarrow x = arctan (a) + 18 0^{\circ} n

θ + 26.56500 \dots^{\circ} = arctan (\frac{156.25}{588.6}) + 18 0^{\circ} n

θ + 26.56500 \dots^{\circ} = arctan (\frac{156.25}{588.6}) + 18 0^{\circ} n

Solve

θ + 26.56500 \dots^{\circ} = arctan (\frac{156.25}{588.6}) + 18 0^{\circ} n : θ = arctan (\frac{156.25}{588.6}) + 18 0^{\circ} n - 26.56500 \dots^{\circ}

θ + 26.56500 \dots^{\circ} = arctan (\frac{156.25}{588.6}) + 18 0^{\circ} n

Move

26.56500 \dots^{\circ}

to the right side

θ + 26.56500 \dots^{\circ} = arctan (\frac{156.25}{588.6}) + 18 0^{\circ} n

Subtract

26.56500 \dots^{\circ}

from both sides

θ + 26.56500 \dots^{\circ} - 26.56500 \dots^{\circ} = arctan (\frac{156.25}{588.6}) + 18 0^{\circ} n - 26.56500 \dots^{\circ}

Simplify

θ = arctan (\frac{156.25}{588.6}) + 18 0^{\circ} n - 26.56500 \dots^{\circ}

θ = arctan (\frac{156.25}{588.6}) + 18 0^{\circ} n - 26.56500 \dots^{\circ}

θ = arctan (\frac{156.25}{588.6}) + 18 0^{\circ} n - 26.56500 \dots^{\circ}

Show solutions in decimal form

θ = 0.25947 \dots + 18 0^{\circ} n - 26.56500 \dots^{\circ}

What is the general solution for tan(θ+26.565)=(12.5^2)/(9.81(60)) ?
The general solution for tan(θ+26.565)=(12.5^2)/(9.81(60)) is θ=0.25947…+180n-26.56500…