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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

3 sin^{2} (x) - 4 cos (x) + 1 = 0

sin (x) - cos (2 x) - 1 = 0

sin^{2} (x) = 3

x, c^{2} = a^{2} + b^{2} - 2 ab \cdot cos (x)

sin (- \frac{π}{8} c) = - \frac{14}{14}

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