What is the general solution for 2cos(θ)=2sin(θ) ?

The general solution for 2cos(θ)=2sin(θ) is θ= pi/4+pin

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2cos(θ)=2sin(θ)

2 cos (θ) = 2 sin (θ)

θ = \frac{π}{4} + πn

Degrees

θ = 4 5^{\circ} + 18 0^{\circ} n

Solution steps

2 cos (θ) = 2 sin (θ)

Rewrite using trig identities

2 cos (θ) = 2 sin (θ)

Divide both sides by

cos (θ), cos (θ) \neq = 0

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

Simplify

2 = \frac{2 sin ( θ )}{cos ( θ )}

Use the basic trigonometric identity:

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

2 = 2 tan (θ)

Switch sides

2 tan (θ) = 2

2 tan (θ) = 2

Divide both sides by

2

2 tan (θ) = 2

Divide both sides by

2

\frac{2 tan ( θ )}{2} = \frac{2}{2}

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

arcsin (x) = \frac{π}{8}

5 tan (x) = 8

3 sin (b) + 3 = 5 sin (b) + 2

8 tan^{2} (θ) + 10 tan (θ) + 10 = 7

3 sec (x) - 23 = 0

What is the general solution for 2cos(θ)=2sin(θ) ?
The general solution for 2cos(θ)=2sin(θ) is θ= pi/4+pin