What is the general solution for ((tan(x))/1)^{-1}=(20)/(9.7) ?

The general solution for ((tan(x))/1)^{-1}=(20)/(9.7) is x=0.45157…+pin

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Popular Trigonometry >

((tan(x))/1)^{-1}=(20)/(9.7)

Solution

(\frac{tan ( x )}{1})^{- 1} = \frac{20}{9.7}

Solution

x = 0.45157 \dots + πn

Degrees

x = 25.87338 \dots^{\circ} + 18 0^{\circ} n

Solution steps

(\frac{tan ( x )}{1})^{- 1} = \frac{20}{9.7}

Refine

\frac{1}{tan ( x )} = \frac{20}{9.7}

Cross multiply

\frac{1}{tan ( x )} = \frac{20}{9.7}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

1 \cdot 9.7 = tan (x) \cdot 20

Simplify

1 \cdot 9.7 : 9.7

1 \cdot 9.7

Multiply the numbers:

1 \cdot 9.7 = 9.7

= 9.7

9.7 = tan (x) \cdot 20

9.7 = tan (x) \cdot 20

Switch sides

tan (x) \cdot 20 = 9.7

Divide both sides by

20

tan (x) \cdot 20 = 9.7

Divide both sides by

20

\frac{tan ( x ) \cdot 20}{20} = \frac{9.7}{20}

Simplify

tan (x) = 0.485

tan (x) = 0.485

Verify Solutions

Find undefined (singularity) points:

tan (x) = 0

Take the denominator(s) of

(\frac{tan ( x )}{1})^{- 1}

and compare to zero

Solve

\frac{tan ( x )}{1} = 0 : tan (x) = 0

\frac{tan ( x )}{1} = 0

Apply rule

\frac{a}{1} = a

tan (x) = 0

The following points are undefined

tan (x) = 0

Combine undefined points with solutions:

tan (x) = 0.485

Apply trig inverse properties

tan (x) = 0.485

General solutions for

tan (x) = 0.485

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

x = arctan (0.485) + πn

x = arctan (0.485) + πn

Show solutions in decimal form

x = 0.45157 \dots + πn

Graph

Popular Examples

1-tan(x)=sec(x)

sec((3θ)/2)=-2,0<= θ<2pi

tan(x-pi/6)=sqrt(3)

2sin(x)tan(x)+5=4sec(x)

cos^2(x)-cos(x)-2=0,0<= x<= 2pi

Frequently Asked Questions (FAQ)

What is the general solution for ((tan(x))/1)^{-1}=(20)/(9.7) ?
The general solution for ((tan(x))/1)^{-1}=(20)/(9.7) is x=0.45157…+pin