What is the general solution for sin(2x)=-5cos(2x) ?

The general solution for sin(2x)=-5cos(2x) is x=-(1.37340…)/2+(pin)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(2x)=-5cos(2x)

sin (2 x) = - 5 cos (2 x)

x = - \frac{1.37340 \dots}{2} + \frac{πn}{2}

Degrees

x = - 39.34503 \dots^{\circ} + 9 0^{\circ} n

Solution steps

sin (2 x) = - 5 cos (2 x)

Rewrite using trig identities

sin (2 x) = - 5 cos (2 x)

Divide both sides by

cos (2 x), cos (2 x) \neq = 0

\frac{sin ( 2 x )}{cos ( 2 x )} = \frac{- 5 cos ( 2 x )}{cos ( 2 x )}

Simplify

\frac{sin ( 2 x )}{cos ( 2 x )} = - 5

Use the basic trigonometric identity:

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

tan (2 x) = - 5

tan (2 x) = - 5

Apply trig inverse properties

tan (2 x) = - 5

General solutions for

tan (2 x) = - 5

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

2 x = arctan (- 5) + πn

2 x = arctan (- 5) + πn

Solve

2 x = arctan (- 5) + πn : x = - \frac{arctan ( 5 )}{2} + \frac{πn}{2}

2 x = arctan (- 5) + πn

Simplify

arctan (- 5) + πn : - arctan (5) + πn

arctan (- 5) + πn

Use the following property:

arctan (- x) = - arctan (x)

arctan (- 5) = - arctan (5)

= - arctan (5) + πn

2 x = - arctan (5) + πn

Divide both sides by

2

2 x = - arctan (5) + πn

Divide both sides by

2

\frac{2 x}{2} = - \frac{arctan ( 5 )}{2} + \frac{πn}{2}

Simplify

x = - \frac{arctan ( 5 )}{2} + \frac{πn}{2}

x = - \frac{arctan ( 5 )}{2} + \frac{πn}{2}

x = - \frac{arctan ( 5 )}{2} + \frac{πn}{2}

Show solutions in decimal form

x = - \frac{1.37340 \dots}{2} + \frac{πn}{2}

tan (x) cot (x) = sec (x) csc (x)

4 sin (x) = cos (x) - 2

sin (θ) = 1 - cos (θ)

cos (θ) - 2 sin (θ) cos (θ) = 0

x, cos (x y) = sin (x + y)

What is the general solution for sin(2x)=-5cos(2x) ?
The general solution for sin(2x)=-5cos(2x) is x=-(1.37340…)/2+(pin)/2