What is the general solution for tan(a)=-1 ?

The general solution for tan(a)=-1 is a=(3pi)/4+pin

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tan(a)=-1

tan (a) = - 1

a = \frac{3 π}{4} + πn

Degrees

a = 13 5^{\circ} + 18 0^{\circ} n

Solution steps

tan (a) = - 1

General solutions for

tan (a) = - 1

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

a = \frac{3 π}{4} + πn

a = \frac{3 π}{4} + πn

cos^{2} (x) + 2 cos (x) = - 1

cot (x) (1 - cos^{2} (x)) = \frac{1}{2} sin^{2} (x)

(tan (x) - 1) (2 sin (x) - 1) = 0

cos (x) = \frac{20}{29}

2 cot^{4} (x) - cot^{2} (x) - 15 = 0

What is the general solution for tan(a)=-1 ?
The general solution for tan(a)=-1 is a=(3pi)/4+pin