What is the general solution for sin(4x)=cos(4x) ?

The general solution for sin(4x)=cos(4x) is x= pi/(16)+(pin)/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(4x)=cos(4x)

sin (4 x) = cos (4 x)

x = \frac{π}{16} + \frac{πn}{4}

Degrees

x = 11.2 5^{\circ} + 4 5^{\circ} n

Solution steps

sin (4 x) = cos (4 x)

Rewrite using trig identities

sin (4 x) = cos (4 x)

Divide both sides by

cos (4 x), cos (4 x) \neq = 0

\frac{sin ( 4 x )}{cos ( 4 x )} = \frac{cos ( 4 x )}{cos ( 4 x )}

Simplify

\frac{sin ( 4 x )}{cos ( 4 x )} = 1

Use the basic trigonometric identity:

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

tan (4 x) = 1

tan (4 x) = 1

General solutions for

tan (4 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}

4 x = \frac{π}{4} + πn

4 x = \frac{π}{4} + πn

Solve

4 x = \frac{π}{4} + πn : x = \frac{π}{16} + \frac{πn}{4}

4 x = \frac{π}{4} + πn

Divide both sides by

4

4 x = \frac{π}{4} + πn

Divide both sides by

4

\frac{4 x}{4} = \frac{\frac{π}{4}}{4} + \frac{πn}{4}

Simplify

\frac{4 x}{4} = \frac{\frac{π}{4}}{4} + \frac{πn}{4}

Simplify

\frac{4 x}{4} : x

\frac{4 x}{4}

Divide the numbers:

\frac{4}{4} = 1

= x

Simplify

\frac{\frac{π}{4}}{4} + \frac{πn}{4} : \frac{π}{16} + \frac{πn}{4}

\frac{\frac{π}{4}}{4} + \frac{πn}{4}

\frac{\frac{π}{4}}{4} = \frac{π}{16}

\frac{\frac{π}{4}}{4}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{4 \cdot 4}

Multiply the numbers:

4 \cdot 4 = 16

= \frac{π}{16}

= \frac{π}{16} + \frac{πn}{4}

x = \frac{π}{16} + \frac{πn}{4}

x = \frac{π}{16} + \frac{πn}{4}

x = \frac{π}{16} + \frac{πn}{4}

x = \frac{π}{16} + \frac{πn}{4}

2 cos^{2} (x) + 9 cos (x) + 4 = 0

x, arccsc (2 x) = \frac{π}{6}

sin^{2} (x) + tan^{2} (x) = 1

cos (6 x) = sin (x - 1)

tan (θ) = \frac{72}{65}

What is the general solution for sin(4x)=cos(4x) ?
The general solution for sin(4x)=cos(4x) is x= pi/(16)+(pin)/4