What is the general solution for 2tan(2x-10)=3.4641 ?

The general solution for 2tan(2x-10)=3.4641 is x=5+(pin)/2+pi/6

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2tan(2x-10)=3.4641

Solution

2 tan (2 x - 10) = 3.4641

Solution

x = 5 + \frac{πn}{2} + \frac{π}{6}

Degrees

x = 316.47889 \dots^{\circ} + 9 0^{\circ} n

Solution steps

2 tan (2 x - 10) = 3.4641

Divide both sides by

2

2 tan (2 x - 10) = 3.4641

Divide both sides by

2

\frac{2 tan ( 2 x - 10 )}{2} = \frac{3.4641}{2}

Simplify

tan (2 x - 10) = \frac{3.4641}{2}

tan (2 x - 10) = \frac{3.4641}{2}

Apply trig inverse properties

tan (2 x - 10) = \frac{3.4641}{2}

General solutions for

tan (2 x - 10) = \frac{3.4641}{2}

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

2 x - 10 = arctan (\frac{3.4641}{2}) + πn

2 x - 10 = arctan (\frac{3.4641}{2}) + πn

Solve

2 x - 10 = arctan (\frac{3.4641}{2}) + πn : x = 5 + \frac{πn}{2} + \frac{π}{6}

2 x - 10 = arctan (\frac{3.4641}{2}) + πn

Simplify

arctan (\frac{3.4641}{2}) + πn : \frac{π}{3} + πn

arctan (\frac{3.4641}{2}) + πn

arctan (\frac{3.4641}{2}) = \frac{π}{3}

arctan (\frac{3.4641}{2})

= arctan (\frac{\frac{34641}{10000}}{2})

Use the following trivial identity:

arctan (\frac{\frac{34641}{10000}}{2}) = \frac{π}{3}

arctan (\frac{\frac{34641}{10000}}{2})

x 0 \frac{3}{3} 13 arctan (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} arctan (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ}

= \frac{π}{3}

= \frac{π}{3}

= \frac{π}{3} + πn

2 x - 10 = \frac{π}{3} + πn

Move

10

to the right side

2 x - 10 = \frac{π}{3} + πn

Add

10

to both sides

2 x - 10 + 10 = \frac{π}{3} + πn + 10

Simplify

2 x = \frac{π}{3} + πn + 10

2 x = \frac{π}{3} + πn + 10

Divide both sides by

2

2 x = \frac{π}{3} + πn + 10

Divide both sides by

2

\frac{2 x}{2} = \frac{\frac{π}{3}}{2} + \frac{πn}{2} + \frac{10}{2}

Simplify

\frac{2 x}{2} = \frac{\frac{π}{3}}{2} + \frac{πn}{2} + \frac{10}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{\frac{π}{3}}{2} + \frac{πn}{2} + \frac{10}{2} : 5 + \frac{πn}{2} + \frac{π}{6}

\frac{\frac{π}{3}}{2} + \frac{πn}{2} + \frac{10}{2}

Group like terms

= \frac{10}{2} + \frac{πn}{2} + \frac{\frac{π}{3}}{2}

\frac{10}{2} = 5

\frac{10}{2}

Divide the numbers:

\frac{10}{2} = 5

= 5

\frac{\frac{π}{3}}{2} = \frac{π}{6}

\frac{\frac{π}{3}}{2}

Apply the fraction rule:

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

= \frac{π}{3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{π}{6}

= 5 + \frac{πn}{2} + \frac{π}{6}

x = 5 + \frac{πn}{2} + \frac{π}{6}

x = 5 + \frac{πn}{2} + \frac{π}{6}

x = 5 + \frac{πn}{2} + \frac{π}{6}

x = 5 + \frac{πn}{2} + \frac{π}{6}

Popular Examples

12cos(pi/3 x)+8=0

12 cos (\frac{π}{3} x) + 8 = 0

(sin(45))/(497.01)=(sin(x))/(450)

\frac{sin ( 4 5 ^{\circ} )}{497.01} = \frac{sin ( x )}{450}

(35)/(sin(A))=(60)/(sin(25))

\frac{35}{sin ( A )} = \frac{60}{sin ( 2 5 ^{\circ} )}

4csc(x)+sin(x)+5=0

4 csc (x) + sin (x) + 5 = 0

tan(x)=1087

tan (x) = 1087

Frequently Asked Questions (FAQ)

What is the general solution for 2tan(2x-10)=3.4641 ?
The general solution for 2tan(2x-10)=3.4641 is x=5+(pin)/2+pi/6