What is the general solution for 3-2cos(x)=3-2sin(x) ?

The general solution for 3-2cos(x)=3-2sin(x) is x= pi/4+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

3-2cos(x)=3-2sin(x)

3 - 2 cos (x) = 3 - 2 sin (x)

x = \frac{π}{4} + πn

Degrees

x = 4 5^{\circ} + 18 0^{\circ} n

Solution steps

3 - 2 cos (x) = 3 - 2 sin (x)

Subtract

3 - 2 sin (x)

from both sides

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

Rewrite using trig identities

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

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

2 tan (x) - 2 = 0

2 tan (x) - 2 = 0

Move

2

to the right side

2 tan (x) - 2 = 0

Add

2

to both sides

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

Simplify

2 tan (x) = 2

2 tan (x) = 2

Divide both sides by

2

2 tan (x) = 2

Divide both sides by

2

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

Simplify

tan (x) = 1

tan (x) = 1

General solutions for

tan (x) = 1

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

3 sin (x) = sin (x) tan (x)

- 2 sin (2 y) = 0

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

4 sin (x - 3 0^{\circ}) - 1.3 = 0

2 cos (\frac{θ}{2}) = cos (θ) + 1

What is the general solution for 3-2cos(x)=3-2sin(x) ?
The general solution for 3-2cos(x)=3-2sin(x) is x= pi/4+pin