What is the general solution for 11sin(θ)=11cos(θ) ?

The general solution for 11sin(θ)=11cos(θ) is θ= pi/4+pin

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11sin(θ)=11cos(θ)

11 sin (θ) = 11 cos (θ)

θ = \frac{π}{4} + πn

Degrees

θ = 4 5^{\circ} + 18 0^{\circ} n

Solution steps

11 sin (θ) = 11 cos (θ)

Rewrite using trig identities

11 sin (θ) = 11 cos (θ)

Divide both sides by

cos (θ), cos (θ) \neq = 0

\frac{11 sin ( θ )}{cos ( θ )} = \frac{11 cos ( θ )}{cos ( θ )}

Simplify

\frac{11 sin ( θ )}{cos ( θ )} = 11

Use the basic trigonometric identity:

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

11 tan (θ) = 11

11 tan (θ) = 11

Divide both sides by

11

11 tan (θ) = 11

Divide both sides by

11

\frac{11 tan ( θ )}{11} = \frac{11}{11}

Simplify

tan (θ) = 1

tan (θ) = 1

General solutions for

tan (θ) = 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}

θ = \frac{π}{4} + πn

θ = \frac{π}{4} + πn

1 - 2 tan (x) = 0

sin (a) = 0.747

1 - tan^{2} (y) = 2 sec (y) - 4

2 sin^{2} (2 θ) + 5 sin (2 θ) = 3

3 cot (x) + 4 = 7

What is the general solution for 11sin(θ)=11cos(θ) ?
The general solution for 11sin(θ)=11cos(θ) is θ= pi/4+pin