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

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

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-cos(x)=sin(x)

- cos (x) = sin (x)

x = \frac{3 π}{4} + πn

Degrees

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

Solution steps

- cos (x) = sin (x)

Rewrite using trig identities

- cos (x) = sin (x)

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

- 1 = tan (x)

Switch sides

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

2 cos^{2} (x) + 5 cos (x) - 3 = 0

x, cos (x) = 1

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

4 sin (x) cos (x) = - 9 cos (x)

cos (t) = - \frac{3}{2}

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