What is the general solution for tan(3x+25)*160-1=0 ?

The general solution for tan(3x+25)*160-1=0 is x=(180n)/3-8.33333…+(0.34387…)/3

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Popular >

tan(3x+25)*160-1=0

Solution

tan (3 x + 2 5^{\circ}) \cdot 16 0^{\circ} - 1 = 0

Solution

x = \frac{18 0 ^{\circ} n}{3} - 8.33333 \dots^{\circ} + \frac{0.34387 \dots}{3}

Radians

x = - \frac{5 π}{108} + \frac{0.34387 \dots}{3} + \frac{π}{3} n

Solution steps

tan (3 x + 2 5^{\circ}) \cdot 16 0^{\circ} - 1 = 0

Move

1

to the right side

tan (3 x + 2 5^{\circ}) 16 0^{\circ} - 1 = 0

Add

1

to both sides

tan (3 x + 2 5^{\circ}) 16 0^{\circ} - 1 + 1 = 0 + 1

Simplify

tan (3 x + 2 5^{\circ}) 16 0^{\circ} = 1

tan (3 x + 2 5^{\circ}) 16 0^{\circ} = 1

Multiply both sides by

9

tan (3 x + 2 5^{\circ}) 16 0^{\circ} = 1

Multiply both sides by

9

9 tan (3 x + 2 5^{\circ}) 16 0^{\circ} = 1 \cdot 9

Simplify

144 0^{\circ} tan (3 x + 2 5^{\circ}) = 9

144 0^{\circ} tan (3 x + 2 5^{\circ}) = 9

Divide both sides by

144 0^{\circ}

144 0^{\circ} tan (3 x + 2 5^{\circ}) = 9

Divide both sides by

144 0^{\circ}

\frac{144 0 ^{\circ} tan ( 3 x + 2 5 ^{\circ} )}{144 0 ^{\circ}} = \frac{9}{144 0 ^{\circ}}

Simplify

tan (3 x + 2 5^{\circ}) = \frac{9}{144 0 ^{\circ}}

tan (3 x + 2 5^{\circ}) = \frac{9}{144 0 ^{\circ}}

Apply trig inverse properties

tan (3 x + 2 5^{\circ}) = \frac{9}{144 0 ^{\circ}}

General solutions for

tan (3 x + 2 5^{\circ}) = \frac{9}{144 0 ^{\circ}}

tan (x) = a \Rightarrow x = arctan (a) + 18 0^{\circ} n

3 x + 2 5^{\circ} = arctan (\frac{9}{144 0 ^{\circ}}) + 18 0^{\circ} n

3 x + 2 5^{\circ} = arctan (\frac{9}{144 0 ^{\circ}}) + 18 0^{\circ} n

Solve

3 x + 2 5^{\circ} = arctan (\frac{9}{144 0 ^{\circ}}) + 18 0^{\circ} n : x = \frac{18 0 ^{\circ} n}{3} - 8.33333 \dots^{\circ} + \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3}

3 x + 2 5^{\circ} = arctan (\frac{9}{144 0 ^{\circ}}) + 18 0^{\circ} n

Move

2 5^{\circ}

to the right side

3 x + 2 5^{\circ} = arctan (\frac{9}{144 0 ^{\circ}}) + 18 0^{\circ} n

Subtract

2 5^{\circ}

from both sides

3 x + 2 5^{\circ} - 2 5^{\circ} = arctan (\frac{9}{144 0 ^{\circ}}) + 18 0^{\circ} n - 2 5^{\circ}

Simplify

3 x = arctan (\frac{9}{144 0 ^{\circ}}) + 18 0^{\circ} n - 2 5^{\circ}

3 x = arctan (\frac{9}{144 0 ^{\circ}}) + 18 0^{\circ} n - 2 5^{\circ}

Divide both sides by

3

3 x = arctan (\frac{9}{144 0 ^{\circ}}) + 18 0^{\circ} n - 2 5^{\circ}

Divide both sides by

3

\frac{3 x}{3} = \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3} + \frac{18 0 ^{\circ} n}{3} - \frac{2 5 ^{\circ}}{3}

Simplify

\frac{3 x}{3} = \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3} + \frac{18 0 ^{\circ} n}{3} - \frac{2 5 ^{\circ}}{3}

Simplify

\frac{3 x}{3} : x

\frac{3 x}{3}

Divide the numbers:

\frac{3}{3} = 1

= x

Simplify

\frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3} + \frac{18 0 ^{\circ} n}{3} - \frac{2 5 ^{\circ}}{3} : \frac{18 0 ^{\circ} n}{3} - 8.33333 \dots^{\circ} + \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3}

\frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3} + \frac{18 0 ^{\circ} n}{3} - \frac{2 5 ^{\circ}}{3}

Group like terms

= \frac{18 0 ^{\circ} n}{3} - \frac{2 5 ^{\circ}}{3} + \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3}

\frac{2 5 ^{\circ}}{3} = 8.33333 \dots^{\circ}

\frac{2 5 ^{\circ}}{3}

Apply the fraction rule:

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

= \frac{90 0 ^{\circ}}{36 \cdot 3}

Multiply the numbers:

36 \cdot 3 = 108

= 8.33333 \dots^{\circ}

= \frac{18 0 ^{\circ} n}{3} - 8.33333 \dots^{\circ} + \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3}

x = \frac{18 0 ^{\circ} n}{3} - 8.33333 \dots^{\circ} + \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3}

x = \frac{18 0 ^{\circ} n}{3} - 8.33333 \dots^{\circ} + \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3}

x = \frac{18 0 ^{\circ} n}{3} - 8.33333 \dots^{\circ} + \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3}

x = \frac{18 0 ^{\circ} n}{3} - 8.33333 \dots^{\circ} + \frac{arctan ( \frac{9}{144 0 ^{\circ}} )}{3}

Show solutions in decimal form

x = \frac{18 0 ^{\circ} n}{3} - 8.33333 \dots^{\circ} + \frac{0.34387 \dots}{3}

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Frequently Asked Questions (FAQ)

What is the general solution for tan(3x+25)*160-1=0 ?
The general solution for tan(3x+25)*160-1=0 is x=(180n)/3-8.33333…+(0.34387…)/3