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

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

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sin(y)=cos(y)

sin (y) = cos (y)

y = \frac{π}{4} + πn

Degrees

y = 4 5^{\circ} + 18 0^{\circ} n

Solution steps

sin (y) = cos (y)

Rewrite using trig identities

sin (y) = cos (y)

Divide both sides by

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

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

Simplify

\frac{sin ( y )}{cos ( y )} = 1

Use the basic trigonometric identity:

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

tan (y) = 1

tan (y) = 1

General solutions for

tan (y) = 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}

y = \frac{π}{4} + πn

y = \frac{π}{4} + πn

\frac{cos ( x )}{sin ( x )} = 2

θ, 2 cos^{2} (θ) + 9 cos (θ) - 5 = 0

tan (3 x) = - 3, 0 \leq x \leq 2 π

5 cos (θ) = - 3

sec^{2} (x) - sec (x) = 0

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