What is the general solution for arctan(sqrt(3/1))=tan(θ) ?

The general solution for arctan(sqrt(3/1))=tan(θ) is θ=0.80844…+pin

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arctan(sqrt(3/1))=tan(θ)

arctan (\frac{3}{1}) = tan (θ)

θ = 0.80844 \dots + πn

Solution steps

arctan (\frac{3}{1}) = tan (θ)

arctan (\frac{3}{1}) = \frac{π}{3}

arctan (\frac{3}{1})

Use the following trivial identity:

arctan (\frac{3}{1}) = \frac{π}{3}

arctan (\frac{3}{1})

x 0 \frac{3}{3} 13 arctan (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} arctan (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ}

= \frac{π}{3}

= \frac{π}{3}

\frac{π}{3} = tan (θ)

Switch sides

tan (θ) = \frac{π}{3}

Apply trig inverse properties

tan (θ) = \frac{π}{3}

General solutions for

tan (θ) = \frac{π}{3}

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

θ = arctan (\frac{π}{3}) + πn

θ = arctan (\frac{π}{3}) + πn

Show solutions in decimal form

θ = 0.80844 \dots + πn

2 sin^{2} (x) - 5 cos (x) + 5 = 0

tan (x) = \frac{20}{40}

2 sin (x + \frac{π}{4}) = 0

sin (x) = \frac{2 ( 5.5 \cdot 1 0 ^{- 7} )}{3.36 \cdot 1 0 ^{- 5}}

sin (x - 3 0^{\circ}) = cos (1 5^{\circ})

What is the general solution for arctan(sqrt(3/1))=tan(θ) ?
The general solution for arctan(sqrt(3/1))=tan(θ) is θ=0.80844…+pin