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

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

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cos(t)=-sin(t)

cos (t) = - sin (t)

t = \frac{3 π}{4} + πn

Degrees

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

Solution steps

cos (t) = - sin (t)

Rewrite using trig identities

cos (t) = - sin (t)

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

1 = - tan (t)

Switch sides

- tan (t) = 1

- tan (t) = 1

Divide both sides by

- 1

- tan (t) = 1

Divide both sides by

- 1

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

Simplify

tan (t) = - 1

tan (t) = - 1

General solutions for

tan (t) = - 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}

t = \frac{3 π}{4} + πn

t = \frac{3 π}{4} + πn

cos (4 x) \cdot 4 = 0

cos^{2} (x) = \frac{3}{2}

sin (\frac{x}{2}) = \frac{3}{5}

16 cos^{2} (x) - 8 = 0

2 sin (4 θ) = 0

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