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

The general solution for cos(x)=2sin(x) is x=0.46364…+pin

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cos(x)=2sin(x)

cos (x) = 2 sin (x)

x = 0.46364 \dots + πn

Degrees

x = 26.56505 \dots^{\circ} + 18 0^{\circ} n

Solution steps

cos (x) = 2 sin (x)

Rewrite using trig identities

cos (x) = 2 sin (x)

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

1 = 2 tan (x)

Switch sides

2 tan (x) = 1

2 tan (x) = 1

Divide both sides by

2

2 tan (x) = 1

Divide both sides by

2

\frac{2 tan ( x )}{2} = \frac{1}{2}

Simplify

tan (x) = \frac{1}{2}

tan (x) = \frac{1}{2}

Apply trig inverse properties

tan (x) = \frac{1}{2}

General solutions for

tan (x) = \frac{1}{2}

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

x = arctan (\frac{1}{2}) + πn

x = arctan (\frac{1}{2}) + πn

Show solutions in decimal form

x = 0.46364 \dots + πn

- 16 sin (4 x) = 0

3 tan (θ) + 1 = 0

2 tan^{2} (x) = 3 sec (x)

cos (θ) + sin (θ) = 0

6 sin (8 x) + 2 = - 3

What is the general solution for cos(x)=2sin(x) ?
The general solution for cos(x)=2sin(x) is x=0.46364…+pin