What is the general solution for solvefor x,sin(x)=-cos(x) ?

The general solution for solvefor x,sin(x)=-cos(x) is x=(3pi)/4+pin

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solvefor x,sin(x)=-cos(x)

solve for

x, sin (x) = - cos (x)

x = \frac{3 π}{4} + πn

Degrees

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

Solution steps

sin (x) = - cos (x)

Rewrite using trig identities

sin (x) = - cos (x)

Divide both sides by

cos (x), cos (x) \neq = 0

\frac{sin ( x )}{cos ( x )} = \frac{- cos ( x )}{cos ( x )}

Simplify

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

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

tan (x) = - 1

tan (x) = - 1

General solutions for

tan (x) = - 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}

x = \frac{3 π}{4} + πn

x = \frac{3 π}{4} + πn

sin (x + \frac{3 π}{2}) = \frac{3}{2}

sin (θ) cos (θ) = \frac{1}{2} cos (θ)

3 sin (x) = 3 + sin (x)

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

2 sin (θ) = 2 sin (θ) cos (θ)

What is the general solution for solvefor x,sin(x)=-cos(x) ?
The general solution for solvefor x,sin(x)=-cos(x) is x=(3pi)/4+pin