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

The general solution for 2cos(θ)=sin(θ) is θ=1.10714…+pin

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2cos(θ)=sin(θ)

2 cos (θ) = sin (θ)

θ = 1.10714 \dots + πn

Degrees

θ = 63.43494 \dots^{\circ} + 18 0^{\circ} n

Solution steps

2 cos (θ) = sin (θ)

Rewrite using trig identities

2 cos (θ) = sin (θ)

Divide both sides by

cos (θ), cos (θ) \neq = 0

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

Simplify

2 = \frac{sin ( θ )}{cos ( θ )}

Use the basic trigonometric identity:

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

2 = tan (θ)

Switch sides

tan (θ) = 2

tan (θ) = 2

Apply trig inverse properties

tan (θ) = 2

General solutions for

tan (θ) = 2

tan (x) = a \Rightarrow x = arctan (a) + πn

θ = arctan (2) + πn

θ = arctan (2) + πn

Show solutions in decimal form

θ = 1.10714 \dots + πn

- 4 cos (c) + 8 = cos (c) + 8

sin (x) = - \frac{3 10}{10}

cos (θ) = \frac{1}{58}

cos (4 x + 4) = sin (10 x + 44)

4 tan^{2} (x) - 3 sec^{2} (x) = 0

What is the general solution for 2cos(θ)=sin(θ) ?
The general solution for 2cos(θ)=sin(θ) is θ=1.10714…+pin