What is the general solution for sin(4x)+cos(4x)=0 ?

The general solution for sin(4x)+cos(4x)=0 is x=(3pi}{16}+\frac{pin)/4

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Popular >

sin(4x)+cos(4x)=0

Solution

sin (4 x) + cos (4 x) = 0

Solution

x = \frac{3 π}{16} + \frac{πn}{4}

Degrees

x = 33.7 5^{\circ} + 4 5^{\circ} n

Solution steps

sin (4 x) + cos (4 x) = 0

Rewrite using trig identities

sin (4 x) + cos (4 x) = 0

Divide both sides by

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

\frac{sin ( 4 x ) + cos ( 4 x )}{cos ( 4 x )} = \frac{0}{cos ( 4 x )}

Simplify

\frac{sin ( 4 x )}{cos ( 4 x )} + 1 = 0

Use the basic trigonometric identity:

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

tan (4 x) + 1 = 0

tan (4 x) + 1 = 0

Move

1

to the right side

tan (4 x) + 1 = 0

Subtract

1

from both sides

tan (4 x) + 1 - 1 = 0 - 1

Simplify

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{3 π}{4} + πn

4 x = \frac{3 π}{4} + πn

Solve

4 x = \frac{3 π}{4} + πn : x = \frac{3 π}{16} + \frac{πn}{4}

4 x = \frac{3 π}{4} + πn

Divide both sides by

4

4 x = \frac{3 π}{4} + πn

Divide both sides by

4

\frac{4 x}{4} = \frac{\frac{3 π}{4}}{4} + \frac{πn}{4}

Simplify

\frac{4 x}{4} = \frac{\frac{3 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{3 π}{4}}{4} + \frac{πn}{4} : \frac{3 π}{16} + \frac{πn}{4}

\frac{\frac{3 π}{4}}{4} + \frac{πn}{4}

\frac{\frac{3 π}{4}}{4} = \frac{3 π}{16}

\frac{\frac{3 π}{4}}{4}

Apply the fraction rule:

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

= \frac{3 π}{4 \cdot 4}

Multiply the numbers:

4 \cdot 4 = 16

= \frac{3 π}{16}

= \frac{3 π}{16} + \frac{πn}{4}

x = \frac{3 π}{16} + \frac{πn}{4}

x = \frac{3 π}{16} + \frac{πn}{4}

x = \frac{3 π}{16} + \frac{πn}{4}

x = \frac{3 π}{16} + \frac{πn}{4}

Popular Examples

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

sin(x)= pi/2

sin (x) = \frac{π}{2}

sin(z)=-5+j^7

sin (z) = - 5 + j^{7}

2cos^2(θ)+5cos(θ)+2=0

2 cos^{2} (θ) + 5 cos (θ) + 2 = 0

sec^2(x)+tan(x)=0

sec^{2} (x) + tan (x) = 0

Frequently Asked Questions (FAQ)

What is the general solution for sin(4x)+cos(4x)=0 ?
The general solution for sin(4x)+cos(4x)=0 is x=(3pi}{16}+\frac{pin)/4