What is the general solution for cot(x/7)=sqrt(12) ?

The general solution for cot(x/7)=sqrt(12) is x=7*0.28103…+7pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cot(x/7)=sqrt(12)

cot (\frac{x}{7}) = 12

x = 7 \cdot 0.28103 \dots + 7 πn

Radians

x = 1.96724 \dots + 21.99114 \dots n

Solution steps

cot (\frac{x}{7}) = 12

Simplify

12 : 23

12

Prime factorization of

12 : 2^{2} \cdot 3

12

12

divides by

212 = 6 \cdot 2

= 2 \cdot 6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 3

= 2^{2} \cdot 3

= 2^{2} \cdot 3

Apply radical rule:

= 3 2^{2}

Apply radical rule:

2^{2} = 2

= 23

Apply trig inverse properties

cot (\frac{x}{7}) = 23

General solutions for

cot (\frac{x}{7}) = 23

cot (x) = a \Rightarrow x = arccot (a) + πn

\frac{x}{7} = arccot (23) + πn

\frac{x}{7} = arccot (23) + πn

Solve

\frac{x}{7} = arccot (23) + πn : x = 7 arccot (23) + 7 πn

\frac{x}{7} = arccot (23) + πn

Multiply both sides by

7

\frac{x}{7} = arccot (23) + πn

Multiply both sides by

7

\frac{7 x}{7} = 7 arccot (23) + 7 πn

Simplify

x = 7 arccot (23) + 7 πn

x = 7 arccot (23) + 7 πn

x = 7 arccot (23) + 7 πn

Show solutions in decimal form

x = 7 \cdot 0.28103 \dots + 7 πn

sin (θ) = \frac{4}{9}

y, x = sec (y)

2 cos^{2} (θ) - cos (θ) - 4 = - 6 cos (θ) - 6

sin (x) + 2 cos (x) = 1

4 tan (2 x) - 4 cot (x) = 0

What is the general solution for cot(x/7)=sqrt(12) ?
The general solution for cot(x/7)=sqrt(12) is x=7*0.28103…+7pin