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

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

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-sin(x)=cos(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

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{3 π}{4} + πn

x = \frac{3 π}{4} + πn

sin (3 x) + sin (x) = 0, 0 \leq x \leq 2 π

4 sin (θ) + 3 = 1

25 cot^{2} (θ) - 1 = 0

cos (a) = \frac{5}{13}

sec (2 x) - 2 = 0

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