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

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

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sin(x)=2cos(x)

sin (x) = 2 cos (x)

x = 1.10714 \dots + πn

Degrees

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

Solution steps

sin (x) = 2 cos (x)

Rewrite using trig identities

sin (x) = 2 cos (x)

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

tan (x) = 2

tan (x) = 2

Apply trig inverse properties

tan (x) = 2

General solutions for

tan (x) = 2

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

x = arctan (2) + πn

x = arctan (2) + πn

Show solutions in decimal form

x = 1.10714 \dots + πn

sec (x) tan (x) = 0

2 cos (x) + 1 = 3

sec (x) + tan (x) = 0

sin (x + \frac{π}{6}) - sin (x - \frac{7 π}{6}) = \frac{3}{2}

3 cos^{2} (x) = sin^{2} (x)

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