What is the general solution for 8tan(θ)-sqrt(54)=0 ?

The general solution for 8tan(θ)-sqrt(54)=0 is θ=0.74297…+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

8tan(θ)-sqrt(54)=0

Solution

8 tan (θ) - 54 = 0

Solution

θ = 0.74297 \dots + πn

Degrees

θ = 42.56929 \dots^{\circ} + 18 0^{\circ} n

Solution steps

8 tan (θ) - 54 = 0

Simplify

8 tan (θ) - 54 : 8 tan (θ) - 36

8 tan (θ) - 54

54 = 36

54

Prime factorization of

54 : 2 \cdot 3^{3}

54

54

divides by

254 = 27 \cdot 2

= 2 \cdot 27

27

divides by

327 = 9 \cdot 3

= 2 \cdot 3 \cdot 9

9

divides by

39 = 3 \cdot 3

= 2 \cdot 3 \cdot 3 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3 \cdot 3 \cdot 3

= 2 \cdot 3^{3}

= 3^{3} \cdot 2

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

= 3^{2} \cdot 2 \cdot 3

Apply radical rule:

= 3^{2} 2 \cdot 3

Apply radical rule:

3^{2} = 3

= 3 2 \cdot 3

Refine

= 36

= 8 tan (θ) - 36

8 tan (θ) - 36 = 0

Move

36

to the right side

8 tan (θ) - 36 = 0

Add

36

to both sides

8 tan (θ) - 36 + 36 = 0 + 36

Simplify

8 tan (θ) = 36

8 tan (θ) = 36

Divide both sides by

8

8 tan (θ) = 36

Divide both sides by

8

\frac{8 tan ( θ )}{8} = \frac{3 6}{8}

Simplify

tan (θ) = \frac{3 6}{8}

tan (θ) = \frac{3 6}{8}

Apply trig inverse properties

tan (θ) = \frac{3 6}{8}

General solutions for

tan (θ) = \frac{3 6}{8}

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

θ = arctan (\frac{3 6}{8}) + πn

θ = arctan (\frac{3 6}{8}) + πn

Show solutions in decimal form

θ = 0.74297 \dots + πn

Popular Examples

3sin^2(x)-3=0

3 sin^{2} (x) - 3 = 0

tan(2x+pi/3)=sqrt(3)

tan (2 x + \frac{π}{3}) = 3

tan(θ)=-8

tan (θ) = - 8

2cos(2θ)+7sin(θ)-2=-2

2 cos (2 θ) + 7 sin (θ) - 2 = - 2

tan(θ)=19

tan (θ) = 19

Frequently Asked Questions (FAQ)

What is the general solution for 8tan(θ)-sqrt(54)=0 ?
The general solution for 8tan(θ)-sqrt(54)=0 is θ=0.74297…+pin