What is the general solution for 4sqrt(3)cos(t)-4sin(t)=0 ?

The general solution for 4sqrt(3)cos(t)-4sin(t)=0 is t= pi/3+pin

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Popular >

4sqrt(3)cos(t)-4sin(t)=0

Solution

43 cos (t) - 4 sin (t) = 0

Solution

t = \frac{π}{3} + πn

Degrees

t = 6 0^{\circ} + 18 0^{\circ} n

Solution steps

43 cos (t) - 4 sin (t) = 0

Rewrite using trig identities

43 cos (t) - 4 sin (t) = 0

Divide both sides by

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

\frac{4 3 cos ( t ) - 4 sin ( t )}{cos ( t )} = \frac{0}{cos ( t )}

Simplify

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

Use the basic trigonometric identity:

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

43 - 4 tan (t) = 0

43 - 4 tan (t) = 0

Move

43

to the right side

43 - 4 tan (t) = 0

Subtract

43

from both sides

43 - 4 tan (t) - 43 = 0 - 43

Simplify

- 4 tan (t) = - 43

- 4 tan (t) = - 43

Divide both sides by

- 4

- 4 tan (t) = - 43

Divide both sides by

- 4

\frac{- 4 tan ( t )}{- 4} = \frac{- 4 3}{- 4}

Simplify

\frac{- 4 tan ( t )}{- 4} = \frac{- 4 3}{- 4}

Simplify

\frac{- 4 tan ( t )}{- 4} : tan (t)

\frac{- 4 tan ( t )}{- 4}

Apply the fraction rule:

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

= \frac{4 tan ( t )}{4}

Divide the numbers:

\frac{4}{4} = 1

= tan (t)

Simplify

\frac{- 4 3}{- 4} : 3

\frac{- 4 3}{- 4}

Apply the fraction rule:

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

= \frac{4 3}{4}

Divide the numbers:

\frac{4}{4} = 1

= 3

tan (t) = 3

tan (t) = 3

tan (t) = 3

General solutions for

tan (t) = 3

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}

t = \frac{π}{3} + πn

t = \frac{π}{3} + πn

Graph

Popular Examples

csc(θ)=-5/2

csc (θ) = - \frac{5}{2}

(sqrt(3))/3 =tan(θ)

\frac{3}{3} = tan (θ)

solvefor x,tan(x)+sqrt(3)=0 solve for

x, tan (x) + 3 = 0

cos(x)=(4.1)/(7.9)

cos (x) = \frac{4.1}{7.9}

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

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

Frequently Asked Questions (FAQ)

What is the general solution for 4sqrt(3)cos(t)-4sin(t)=0 ?
The general solution for 4sqrt(3)cos(t)-4sin(t)=0 is t= pi/3+pin