What is the general solution for -7sqrt(3)tan(θ)+5=26 ?

The general solution for -7sqrt(3)tan(θ)+5=26 is θ=(2pi)/3+pin

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Popular >

-7sqrt(3)tan(θ)+5=26

Solution

- 73 tan (θ) + 5 = 26

Solution

θ = \frac{2 π}{3} + πn

Degrees

θ = 12 0^{\circ} + 18 0^{\circ} n

Solution steps

- 73 tan (θ) + 5 = 26

Move

5

to the right side

- 73 tan (θ) + 5 = 26

Subtract

5

from both sides

- 73 tan (θ) + 5 - 5 = 26 - 5

Simplify

- 73 tan (θ) = 21

- 73 tan (θ) = 21

Divide both sides by

- 73

- 73 tan (θ) = 21

Divide both sides by

- 73

\frac{- 7 3 tan ( θ )}{- 7 3} = \frac{21}{- 7 3}

Simplify

\frac{- 7 3 tan ( θ )}{- 7 3} = \frac{21}{- 7 3}

Simplify

\frac{- 7 3 tan ( θ )}{- 7 3} : tan (θ)

\frac{- 7 3 tan ( θ )}{- 7 3}

Apply the fraction rule:

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

= \frac{7 3 tan ( θ )}{7 3}

Divide the numbers:

\frac{7}{7} = 1

= \frac{3 tan ( θ )}{3}

Cancel the common factor:

3

= tan (θ)

Simplify

\frac{21}{- 7 3} : - 3

\frac{21}{- 7 3}

Apply the fraction rule:

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

= - \frac{21}{7 3}

Divide the numbers:

\frac{21}{7} = 3

= \frac{3}{3}

Apply radical rule:

3 = 3^{\frac{1}{2}}

= \frac{3}{3 ^{\frac{1}{2}}}

Apply exponent rule:

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

\frac{3 ^{1}}{3 ^{\frac{1}{2}}} = 3^{1 - \frac{1}{2}}

= 3^{1 - \frac{1}{2}}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= 3^{\frac{1}{2}}

Apply radical rule:

3^{\frac{1}{2}} = 3

= - 3

tan (θ) = - 3

tan (θ) = - 3

tan (θ) = - 3

General solutions for

tan (θ) = - 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}

θ = \frac{2 π}{3} + πn

θ = \frac{2 π}{3} + πn

Popular Examples

6sin(x)=cos(x)-3

6 sin (x) = cos (x) - 3

-2sin(4x)=0

- 2 sin (4 x) = 0

2sin(x)+sqrt(3)=0,0<= x<= 2pi

2 sin (x) + 3 = 0, 0 \leq x \leq 2 π

cos(2x)=1-sin(2x),0<= x<= 2pi

cos (2 x) = 1 - sin (2 x), 0 \leq x \leq 2 π

0=1+2sin(θ)

0 = 1 + 2 sin (θ)

Frequently Asked Questions (FAQ)

What is the general solution for -7sqrt(3)tan(θ)+5=26 ?
The general solution for -7sqrt(3)tan(θ)+5=26 is θ=(2pi)/3+pin