What is the general solution for tan(θ)= 1/(sqrt(2)) ?

The general solution for tan(θ)= 1/(sqrt(2)) is θ=0.61547…+pin

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tan(θ)= 1/(sqrt(2))

tan (θ) = \frac{1}{2}

θ = 0.61547 \dots + πn

Solution steps

tan (θ) = \frac{1}{2}

Simplify

\frac{1}{2} : \frac{2}{2}

\frac{1}{2}

Multiply by the conjugate

\frac{2}{2}

= \frac{1 \cdot 2}{2 2}

1 \cdot 2 = 2

22 = 2

22

Apply radical rule:

a a = a

22 = 2

= 2

= \frac{2}{2}

tan (θ) = \frac{2}{2}

Apply trig inverse properties

tan (θ) = \frac{2}{2}

General solutions for

tan (θ) = \frac{2}{2}

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

θ = arctan (\frac{2}{2}) + πn

θ = arctan (\frac{2}{2}) + πn

Show solutions in decimal form

θ = 0.61547 \dots + πn

- cos (x) - sin (x) = 1

sin (2 x) = sin (0.5 x)

2 sin (2 x + 15) = \frac{1}{2}

sin^{2} (x) - 2 cos^{4} (x) = 0

2 cos^{2} (θ) - 1 = sec (θ)

What is the general solution for tan(θ)= 1/(sqrt(2)) ?
The general solution for tan(θ)= 1/(sqrt(2)) is θ=0.61547…+pin