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

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

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tan(φ)=-1/(sqrt(2))

tan (φ) = - \frac{1}{2}

φ = - 0.61547 \dots + πn

Solution steps

tan (φ) = - \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 (φ) = - \frac{2}{2}

Apply trig inverse properties

tan (φ) = - \frac{2}{2}

General solutions for

tan (φ) = - \frac{2}{2}

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

φ = arctan (- \frac{2}{2}) + πn

φ = arctan (- \frac{2}{2}) + πn

Show solutions in decimal form

φ = - 0.61547 \dots + πn

cos (θ) = \frac{1}{10}

2 = 2 sin (x)

cos^{2} (θ) + 2 cos (θ) + 1 = 0, 0 \leq θ \leq 2 π

cot (θ) - 3 = 0, 0 \leq θ \leq 2 π

2 = sec (θ)

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