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

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

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-sin(x)=-cos(x)

- sin (x) = - cos (x)

x = \frac{π}{4} + πn

Degrees

x = 4 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

Divide both sides by

- 1

- tan (x) = - 1

Divide both sides by

- 1

\frac{- tan ( x )}{- 1} = \frac{- 1}{- 1}

Simplify

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{π}{4} + πn

x = \frac{π}{4} + πn

t, f = sin (k t)

6 sin (θ) = 3 + 3 sin (θ)

sin (θ) = \frac{- 2}{2 2}, 0 \leq θ < 2 π

(sin (θ) + 1) (sin (θ) - 1) = 0

\frac{30}{sin ( x )} = \frac{50}{sin ( 9 0 ^{\circ} )}

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