What is the general solution for 2sin(x)-cos(x)=0,0<= x<= 360 ?

The general solution for 2sin(x)-cos(x)=0,0<= x<= 360 is x=0.46364…,x=0.46364…+180

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2sin(x)-cos(x)=0,0<= x<= 360

2 sin (x) - cos (x) = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

x = 0.46364 \dots, x = 0.46364 \dots + 18 0^{\circ}

Radians

x = 0.46364 \dots, x = 0.46364 \dots + π

Solution steps

2 sin (x) - cos (x) = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

Rewrite using trig identities

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

Divide both sides by

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

\frac{2 sin ( x ) - cos ( x )}{cos ( x )} = \frac{0}{cos ( x )}

Simplify

\frac{2 sin ( x )}{cos ( x )} - 1 = 0

Use the basic trigonometric identity:

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

2 tan (x) - 1 = 0

2 tan (x) - 1 = 0

Move

1

to the right side

2 tan (x) - 1 = 0

Add

1

to both sides

2 tan (x) - 1 + 1 = 0 + 1

Simplify

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) + 18 0^{\circ} n

x = arctan (\frac{1}{2}) + 18 0^{\circ} n

x = arctan (\frac{1}{2}) + 18 0^{\circ} n

Solutions for the range

0 \leq x \leq 36 0^{\circ}

x = arctan (\frac{1}{2}), x = arctan (\frac{1}{2}) + 18 0^{\circ}

Show solutions in decimal form

x = 0.46364 \dots, x = 0.46364 \dots + 18 0^{\circ}

8 tan (A) + 3 = 2 tan (A) + 3

cosh (x) = 3

2 sec (x) + 1 = 0

cot (x) = - 3

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

What is the general solution for 2sin(x)-cos(x)=0,0<= x<= 360 ?
The general solution for 2sin(x)-cos(x)=0,0<= x<= 360 is x=0.46364…,x=0.46364…+180