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

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

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Popular >

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

Solution

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

Solution

t = \frac{3 π}{16} + \frac{πn}{4}

Degrees

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

Solution steps

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

Rewrite using trig identities

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

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

1 + tan (4 t) = 0

1 + tan (4 t) = 0

Move

1

to the right side

1 + tan (4 t) = 0

Subtract

1

from both sides

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

Simplify

tan (4 t) = - 1

tan (4 t) = - 1

General solutions for

tan (4 t) = - 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 t = \frac{3 π}{4} + πn

4 t = \frac{3 π}{4} + πn

Solve

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

4 t = \frac{3 π}{4} + πn

Divide both sides by

4

4 t = \frac{3 π}{4} + πn

Divide both sides by

4

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

Simplify

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

Simplify

\frac{4 t}{4} : t

\frac{4 t}{4}

Divide the numbers:

\frac{4}{4} = 1

= t

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}

t = \frac{3 π}{16} + \frac{πn}{4}

t = \frac{3 π}{16} + \frac{πn}{4}

t = \frac{3 π}{16} + \frac{πn}{4}

t = \frac{3 π}{16} + \frac{πn}{4}

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sin(4x-22)=cos(6x-13)

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csc(x)=-3/(sqrt(5))

csc (x) = - \frac{3}{5}

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cos (x) = \frac{3}{5}, cos (2 π + x)

Frequently Asked Questions (FAQ)

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