What is the general solution for tan(3x+pi/2)=-1 ?

The general solution for tan(3x+pi/2)=-1 is x=(pin)/3+pi/(12)

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tan(3x+pi/2)=-1

Solution

tan (3 x + \frac{π}{2}) = - 1

Solution

x = \frac{πn}{3} + \frac{π}{12}

Degrees

x = 1 5^{\circ} + 6 0^{\circ} n

Solution steps

tan (3 x + \frac{π}{2}) = - 1

General solutions for

tan (3 x + \frac{π}{2}) = - 1

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}

3 x + \frac{π}{2} = \frac{3 π}{4} + πn

3 x + \frac{π}{2} = \frac{3 π}{4} + πn

Solve

3 x + \frac{π}{2} = \frac{3 π}{4} + πn : x = \frac{πn}{3} + \frac{π}{12}

3 x + \frac{π}{2} = \frac{3 π}{4} + πn

Move

\frac{π}{2}

to the right side

3 x + \frac{π}{2} = \frac{3 π}{4} + πn

Subtract

\frac{π}{2}

from both sides

3 x + \frac{π}{2} - \frac{π}{2} = \frac{3 π}{4} + πn - \frac{π}{2}

Simplify

3 x + \frac{π}{2} - \frac{π}{2} = \frac{3 π}{4} + πn - \frac{π}{2}

Simplify

3 x + \frac{π}{2} - \frac{π}{2} : 3 x

3 x + \frac{π}{2} - \frac{π}{2}

Add similar elements:

\frac{π}{2} - \frac{π}{2} = 0

= 3 x

Simplify

\frac{3 π}{4} + πn - \frac{π}{2} : πn + \frac{π}{4}

\frac{3 π}{4} + πn - \frac{π}{2}

Group like terms

= πn - \frac{π}{2} + \frac{3 π}{4}

Least Common Multiplier of

2, 4 : 4

2, 4

Least Common Multiplier (LCM)

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

Multiply each factor the greatest number of times it occurs in either

2

4

= 2 \cdot 2

Multiply the numbers:

2 \cdot 2 = 4

= 4

Adjust Fractions based on the LCM

Multiply each numerator by the same amount needed to multiply its

corresponding denominator to turn it into the LCM

4

For

\frac{π}{2} :

multiply the denominator and numerator by

2

\frac{π}{2} = \frac{π 2}{2 \cdot 2} = \frac{π 2}{4}

= - \frac{π 2}{4} + \frac{3 π}{4}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- π 2 + 3 π}{4}

Add similar elements:

- 2 π + 3 π = π

= πn + \frac{π}{4}

3 x = πn + \frac{π}{4}

3 x = πn + \frac{π}{4}

3 x = πn + \frac{π}{4}

Divide both sides by

3

3 x = πn + \frac{π}{4}

Divide both sides by

3

\frac{3 x}{3} = \frac{πn}{3} + \frac{\frac{π}{4}}{3}

Simplify

\frac{3 x}{3} = \frac{πn}{3} + \frac{\frac{π}{4}}{3}

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

\frac{πn}{3} + \frac{\frac{π}{4}}{3} : \frac{πn}{3} + \frac{π}{12}

\frac{πn}{3} + \frac{\frac{π}{4}}{3}

\frac{\frac{π}{4}}{3} = \frac{π}{12}

\frac{\frac{π}{4}}{3}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{4 \cdot 3}

Multiply the numbers:

4 \cdot 3 = 12

= \frac{π}{12}

= \frac{πn}{3} + \frac{π}{12}

x = \frac{πn}{3} + \frac{π}{12}

x = \frac{πn}{3} + \frac{π}{12}

x = \frac{πn}{3} + \frac{π}{12}

x = \frac{πn}{3} + \frac{π}{12}

Popular Examples

15=60sin(pi/(15[0-d]))+75

15 = 60 sin (\frac{π}{15 [ 0 - d ]}) + 75

cos(θ)=(2sqrt(5))/(sqrt(58))

cos (θ) = \frac{2 5}{58}

tan(θ)=(m^2-m^1)/(1+m^2*m^1),m^2

tan (θ) = \frac{m ^{2} - m ^{1}}{1 + m ^{2} \cdot m ^{1}}, m^{2}

0=-1-tan^2(θ)+2tan(θ)

0 = - 1 - tan^{2} (θ) + 2 tan (θ)

solvefor u,x=tanh(u)solve for

u, x = tanh (u)

Frequently Asked Questions (FAQ)

What is the general solution for tan(3x+pi/2)=-1 ?
The general solution for tan(3x+pi/2)=-1 is x=(pin)/3+pi/(12)