What is the general solution for tan(2x-5)=1 ?

The general solution for tan(2x-5)=1 is x= 5/2+pi/8+(pin)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan(2x-5)=1

tan (2 x - 5) = 1

x = \frac{5}{2} + \frac{π}{8} + \frac{πn}{2}

Degrees

x = 165.73944 \dots^{\circ} + 9 0^{\circ} n

Solution steps

tan (2 x - 5) = 1

General solutions for

tan (2 x - 5) = 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}

2 x - 5 = \frac{π}{4} + πn

2 x - 5 = \frac{π}{4} + πn

Solve

2 x - 5 = \frac{π}{4} + πn : x = \frac{5}{2} + \frac{π}{8} + \frac{πn}{2}

2 x - 5 = \frac{π}{4} + πn

Move

5

to the right side

2 x - 5 = \frac{π}{4} + πn

Add

5

to both sides

2 x - 5 + 5 = \frac{π}{4} + πn + 5

Simplify

2 x = \frac{π}{4} + πn + 5

2 x = \frac{π}{4} + πn + 5

Divide both sides by

2

2 x = \frac{π}{4} + πn + 5

Divide both sides by

2

\frac{2 x}{2} = \frac{\frac{π}{4}}{2} + \frac{πn}{2} + \frac{5}{2}

Simplify

\frac{2 x}{2} = \frac{\frac{π}{4}}{2} + \frac{πn}{2} + \frac{5}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{\frac{π}{4}}{2} + \frac{πn}{2} + \frac{5}{2} : \frac{5}{2} + \frac{π}{8} + \frac{πn}{2}

\frac{\frac{π}{4}}{2} + \frac{πn}{2} + \frac{5}{2}

Group like terms

= \frac{5}{2} + \frac{πn}{2} + \frac{\frac{π}{4}}{2}

\frac{\frac{π}{4}}{2} = \frac{π}{8}

\frac{\frac{π}{4}}{2}

Apply the fraction rule:

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

= \frac{π}{4 \cdot 2}

Multiply the numbers:

4 \cdot 2 = 8

= \frac{π}{8}

= \frac{5}{2} + \frac{πn}{2} + \frac{π}{8}

Group like terms

= \frac{5}{2} + \frac{π}{8} + \frac{πn}{2}

x = \frac{5}{2} + \frac{π}{8} + \frac{πn}{2}

x = \frac{5}{2} + \frac{π}{8} + \frac{πn}{2}

x = \frac{5}{2} + \frac{π}{8} + \frac{πn}{2}

x = \frac{5}{2} + \frac{π}{8} + \frac{πn}{2}

\frac{5}{21 \cdot 30} = cos (x)

cos^{2} (x) = \frac{( 7 k - 7 )}{3}

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

(cos (x) + 1) (sin (x) - \frac{1}{2}) = 0

cos (2 x) = \frac{( 6 k - 9 )}{10}

What is the general solution for tan(2x-5)=1 ?
The general solution for tan(2x-5)=1 is x= 5/2+pi/8+(pin)/2