What is the general solution for solvefor a,s(t)=tan(at+pi) ?

The general solution for solvefor a,s(t)=tan(at+pi) is a=(arctan(st))/t+(pin)/t-pi/t

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solvefor a,s(t)=tan(at+pi)

solve for

a, s (t) = tan (a t + π)

a = \frac{arctan ( s t )}{t} + \frac{πn}{t} - \frac{π}{t}

Solution steps

s (t) = tan (a t + π)

Switch sides

tan (a t + π) = s t

Apply trig inverse properties

tan (a t + π) = s t

General solutions for

tan (a t + π) = s t

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

a t + π = arctan (s t) + πn

a t + π = arctan (s t) + πn

Solve

a t + π = arctan (s t) + πn : a = \frac{arctan ( s t )}{t} + \frac{πn}{t} - \frac{π}{t}; t \neq = 0

a t + π = arctan (s t) + πn

Move

π

to the right side

a t + π = arctan (s t) + πn

Subtract

π

from both sides

a t + π - π = arctan (s t) + πn - π

Simplify

a t = arctan (s t) + πn - π

a t = arctan (s t) + πn - π

Divide both sides by

t; t \neq = 0

a t = arctan (s t) + πn - π

Divide both sides by

t; t \neq = 0

\frac{a t}{t} = \frac{arctan ( s t )}{t} + \frac{πn}{t} - \frac{π}{t}; t \neq = 0

Simplify

a = \frac{arctan ( s t )}{t} + \frac{πn}{t} - \frac{π}{t}; t \neq = 0

a = \frac{arctan ( s t )}{t} + \frac{πn}{t} - \frac{π}{t}; t \neq = 0

a = \frac{arctan ( s t )}{t} + \frac{πn}{t} - \frac{π}{t}

0 = sec (x) tan (x)

sin (x - \frac{π}{2}) tan (x) = sin (x)

8 sin (x) + 12 = 16

cos (7 x) = - 1

8 sin (t) + 8 cos (t) = 8

What is the general solution for solvefor a,s(t)=tan(at+pi) ?
The general solution for solvefor a,s(t)=tan(at+pi) is a=(arctan(st))/t+(pin)/t-pi/t