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

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

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cos(t)=sin(t)

cos (t) = sin (t)

t = \frac{π}{4} + πn

Degrees

t = 4 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

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{π}{4} + πn

t = \frac{π}{4} + πn

2 cos (3 x) = 0

16 cos^{2} (θ) - 2 = 0

2 tan^{2} (θ) - 5 tan (θ) + 4 = - 8 tan (θ) + 6

1 + \frac{tan ^{2} ( θ )}{sec ( θ )} = sec (θ)

170 = \frac{16 0 ^{2}}{32} sin (2 θ)

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