What is the general solution for tan(θ)=(3/1-2/5)/(1+3/1*2/5) ?

The general solution for tan(θ)=(3/1-2/5)/(1+3/1*2/5) is θ=0.86853…+pin

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tan(θ)=(3/1-2/5)/(1+3/1*2/5)

tan (θ) = \frac{\frac{3}{1} - \frac{2}{5}}{1 + \frac{3}{1} \cdot \frac{2}{5}}

θ = 0.86853 \dots + πn

Solution steps

tan (θ) = \frac{\frac{3}{1} - \frac{2}{5}}{1 + \frac{3}{1} \cdot \frac{2}{5}}

Simplify

\frac{\frac{3}{1} - \frac{2}{5}}{1 + \frac{3}{1} \cdot \frac{2}{5}} : \frac{13}{11}

\frac{\frac{3}{1} - \frac{2}{5}}{1 + \frac{3}{1} \cdot \frac{2}{5}}

Apply rule

\frac{a}{1} = a

= \frac{3 - \frac{2}{5}}{1 + 3 \cdot \frac{2}{5}}

3 \cdot \frac{2}{5} = \frac{6}{5}

3 \cdot \frac{2}{5}

Multiply fractions:

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

= \frac{2 \cdot 3}{5}

Multiply the numbers:

2 \cdot 3 = 6

= \frac{6}{5}

= \frac{3 - \frac{2}{5}}{1 + \frac{6}{5}}

Join

3 - \frac{2}{5} : \frac{13}{5}

3 - \frac{2}{5}

Convert element to fraction:

3 = \frac{3 \cdot 5}{5}

= \frac{3 \cdot 5}{5} - \frac{2}{5}

Since the denominators are equal, combine the fractions:

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

= \frac{3 \cdot 5 - 2}{5}

3 \cdot 5 - 2 = 13

3 \cdot 5 - 2

Multiply the numbers:

3 \cdot 5 = 15

= 15 - 2

Subtract the numbers:

15 - 2 = 13

= 13

= \frac{13}{5}

= \frac{\frac{13}{5}}{1 + \frac{6}{5}}

Apply the fraction rule:

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

= \frac{13}{5 ( 1 + \frac{6}{5} )}

Join

1 + \frac{6}{5} : \frac{11}{5}

1 + \frac{6}{5}

Convert element to fraction:

1 = \frac{1 \cdot 5}{5}

= \frac{1 \cdot 5}{5} + \frac{6}{5}

Since the denominators are equal, combine the fractions:

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

= \frac{1 \cdot 5 + 6}{5}

1 \cdot 5 + 6 = 11

1 \cdot 5 + 6

Multiply the numbers:

1 \cdot 5 = 5

= 5 + 6

Add the numbers:

5 + 6 = 11

= 11

= \frac{11}{5}

= \frac{13}{5 \cdot \frac{11}{5}}

Multiply

5 \cdot \frac{11}{5} : 11

5 \cdot \frac{11}{5}

Multiply fractions:

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

= \frac{11 \cdot 5}{5}

Cancel the common factor:

5

= 11

= \frac{13}{11}

tan (θ) = \frac{13}{11}

Apply trig inverse properties

tan (θ) = \frac{13}{11}

General solutions for

tan (θ) = \frac{13}{11}

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

θ = arctan (\frac{13}{11}) + πn

θ = arctan (\frac{13}{11}) + πn

Show solutions in decimal form

θ = 0.86853 \dots + πn

tan (t) = 14

cos (A) = \frac{5}{8}

sin (9 x + 40) = cos (- 5 x + 42)

sin^{2} (a) = - \frac{( 5 11 )}{( 18 )}

3.87 sin (\frac{2 π ( t + 101.75 )}{365}) + 11.7 = 14

What is the general solution for tan(θ)=(3/1-2/5)/(1+3/1*2/5) ?
The general solution for tan(θ)=(3/1-2/5)/(1+3/1*2/5) is θ=0.86853…+pin