What is the general solution for 3cos(20t)+6sin(20t)=0 ?

The general solution for 3cos(20t)+6sin(20t)=0 is t=-(0.46364…)/(20)+(pin)/(20)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

3cos(20t)+6sin(20t)=0

Solution

3 cos (20 t) + 6 sin (20 t) = 0

Solution

t = - \frac{0.46364 \dots}{20} + \frac{πn}{20}

Degrees

t = - 1.32825 \dots^{\circ} + 9^{\circ} n

Solution steps

3 cos (20 t) + 6 sin (20 t) = 0

Rewrite using trig identities

3 cos (20 t) + 6 sin (20 t) = 0

Divide both sides by

cos (20 t), cos (20 t) \neq = 0

\frac{3 cos ( 20 t ) + 6 sin ( 20 t )}{cos ( 20 t )} = \frac{0}{cos ( 20 t )}

Simplify

3 + \frac{6 sin ( 20 t )}{cos ( 20 t )} = 0

Use the basic trigonometric identity:

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

3 + 6 tan (20 t) = 0

3 + 6 tan (20 t) = 0

Move

3

to the right side

3 + 6 tan (20 t) = 0

Subtract

3

from both sides

3 + 6 tan (20 t) - 3 = 0 - 3

Simplify

6 tan (20 t) = - 3

6 tan (20 t) = - 3

Divide both sides by

6

6 tan (20 t) = - 3

Divide both sides by

6

\frac{6 tan ( 20 t )}{6} = \frac{- 3}{6}

Simplify

\frac{6 tan ( 20 t )}{6} = \frac{- 3}{6}

Simplify

\frac{6 tan ( 20 t )}{6} : tan (20 t)

\frac{6 tan ( 20 t )}{6}

Divide the numbers:

\frac{6}{6} = 1

= tan (20 t)

Simplify

\frac{- 3}{6} : - \frac{1}{2}

\frac{- 3}{6}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{3}{6}

Cancel the common factor:

3

= - \frac{1}{2}

tan (20 t) = - \frac{1}{2}

tan (20 t) = - \frac{1}{2}

tan (20 t) = - \frac{1}{2}

Apply trig inverse properties

tan (20 t) = - \frac{1}{2}

General solutions for

tan (20 t) = - \frac{1}{2}

tan (x) = - a \Rightarrow x = arctan (- a) + πn

20 t = arctan (- \frac{1}{2}) + πn

20 t = arctan (- \frac{1}{2}) + πn

Solve

20 t = arctan (- \frac{1}{2}) + πn : t = - \frac{arctan ( \frac{1}{2} )}{20} + \frac{πn}{20}

20 t = arctan (- \frac{1}{2}) + πn

Simplify

arctan (- \frac{1}{2}) + πn : - arctan (\frac{1}{2}) + πn

arctan (- \frac{1}{2}) + πn

Use the following property:

arctan (- x) = - arctan (x)

arctan (- \frac{1}{2}) = - arctan (\frac{1}{2})

= - arctan (\frac{1}{2}) + πn

20 t = - arctan (\frac{1}{2}) + πn

Divide both sides by

20

20 t = - arctan (\frac{1}{2}) + πn

Divide both sides by

20

\frac{20 t}{20} = - \frac{arctan ( \frac{1}{2} )}{20} + \frac{πn}{20}

Simplify

t = - \frac{arctan ( \frac{1}{2} )}{20} + \frac{πn}{20}

t = - \frac{arctan ( \frac{1}{2} )}{20} + \frac{πn}{20}

t = - \frac{arctan ( \frac{1}{2} )}{20} + \frac{πn}{20}

Show solutions in decimal form

t = - \frac{0.46364 \dots}{20} + \frac{πn}{20}

Popular Examples

tan(θ)= 6/2

tan (θ) = \frac{6}{2}

tan(θ)= 6/4

tan (θ) = \frac{6}{4}

2cot^2(x)+3csc(x)=0

2 cot^{2} (x) + 3 csc (x) = 0

solvefor t,f=2sin(kt)solve for

t, f = 2 sin (k t)

cos(((2x-pi))/4)=1

cos (\frac{( 2 x - π )}{4}) = 1

Frequently Asked Questions (FAQ)

What is the general solution for 3cos(20t)+6sin(20t)=0 ?
The general solution for 3cos(20t)+6sin(20t)=0 is t=-(0.46364…)/(20)+(pin)/(20)