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

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

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cos(φ)=sin(φ)

cos (φ) = sin (φ)

φ = \frac{π}{4} + πn

Degrees

φ = 4 5^{\circ} + 18 0^{\circ} n

Solution steps

cos (φ) = sin (φ)

Rewrite using trig identities

cos (φ) = sin (φ)

Divide both sides by

cos (φ), cos (φ) \neq = 0

\frac{cos ( φ )}{cos ( φ )} = \frac{sin ( φ )}{cos ( φ )}

Simplify

1 = \frac{sin ( φ )}{cos ( φ )}

Use the basic trigonometric identity:

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

1 = tan (φ)

Switch sides

tan (φ) = 1

tan (φ) = 1

General solutions for

tan (φ) = 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}

φ = \frac{π}{4} + πn

φ = \frac{π}{4} + πn

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