What is the general solution for 1-tan(a)=(-1)/3 ?

The general solution for 1-tan(a)=(-1)/3 is a=0.92729…+pin

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Popular >

1-tan(a)=(-1)/3

Solution

1 - tan (a) = \frac{- 1}{3}

Solution

a = 0.92729 \dots + πn

Degrees

a = 53.13010 \dots^{\circ} + 18 0^{\circ} n

Solution steps

1 - tan (a) = \frac{- 1}{3}

Move

1

to the right side

1 - tan (a) = \frac{- 1}{3}

Subtract

1

from both sides

1 - tan (a) - 1 = \frac{- 1}{3} - 1

Simplify

1 - tan (a) - 1 = \frac{- 1}{3} - 1

Simplify

1 - tan (a) - 1 : - tan (a)

1 - tan (a) - 1

Add similar elements:

1 - 1 = 0

= - tan (a)

Simplify

\frac{- 1}{3} - 1 : - \frac{4}{3}

\frac{- 1}{3} - 1

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{1}{3} - 1

Convert element to fraction:

1 = \frac{1 \cdot 3}{3}

= - \frac{1 \cdot 3}{3} - \frac{1}{3}

Since the denominators are equal, combine the fractions:

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

= \frac{- 1 \cdot 3 - 1}{3}

- 1 \cdot 3 - 1 = - 4

- 1 \cdot 3 - 1

Multiply the numbers:

1 \cdot 3 = 3

= - 3 - 1

Subtract the numbers:

- 3 - 1 = - 4

= - 4

= \frac{- 4}{3}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{4}{3}

- tan (a) = - \frac{4}{3}

- tan (a) = - \frac{4}{3}

- tan (a) = - \frac{4}{3}

Divide both sides by

- 1

- tan (a) = - \frac{4}{3}

Divide both sides by

- 1

\frac{- tan ( a )}{- 1} = \frac{- \frac{4}{3}}{- 1}

Simplify

\frac{- tan ( a )}{- 1} = \frac{- \frac{4}{3}}{- 1}

Simplify

\frac{- tan ( a )}{- 1} : tan (a)

\frac{- tan ( a )}{- 1}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{tan ( a )}{1}

Apply rule

\frac{a}{1} = a

= tan (a)

Simplify

\frac{- \frac{4}{3}}{- 1} : \frac{4}{3}

\frac{- \frac{4}{3}}{- 1}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{\frac{4}{3}}{1}

Apply the fraction rule:

\frac{a}{1} = a

= \frac{4}{3}

tan (a) = \frac{4}{3}

tan (a) = \frac{4}{3}

tan (a) = \frac{4}{3}

Apply trig inverse properties

tan (a) = \frac{4}{3}

General solutions for

tan (a) = \frac{4}{3}

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

a = arctan (\frac{4}{3}) + πn

a = arctan (\frac{4}{3}) + πn

Show solutions in decimal form

a = 0.92729 \dots + πn

Popular Examples

tan^2(x)+cos^2(x)-1=0

tan^{2} (x) + cos^{2} (x) - 1 = 0

cot^3(x)+cot(x)=0

cot^{3} (x) + cot (x) = 0

21+18cos(x)=16(1-cos^2(x))

21 + 18 cos (x) = 16 (1 - cos^{2} (x))

sin(2a+10)=cos(3a-20)

sin (2 a + 10) = cos (3 a - 20)

b= 3/((cot(x)))

b = \frac{3}{( cot ( x ) )}

Frequently Asked Questions (FAQ)

What is the general solution for 1-tan(a)=(-1)/3 ?
The general solution for 1-tan(a)=(-1)/3 is a=0.92729…+pin