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

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

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cos(a)=-sin(a)

cos (a) = - sin (a)

a = \frac{3 π}{4} + πn

Degrees

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

Solution steps

cos (a) = - sin (a)

Rewrite using trig identities

cos (a) = - sin (a)

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

1 = - tan (a)

Switch sides

- tan (a) = 1

- tan (a) = 1

Divide both sides by

- 1

- tan (a) = 1

Divide both sides by

- 1

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

Simplify

tan (a) = - 1

tan (a) = - 1

General solutions for

tan (a) = - 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}

a = \frac{3 π}{4} + πn

a = \frac{3 π}{4} + πn

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