What is the general solution for solvefor x,tan(2x)=-(((30+20)/2))/(80) ?

The general solution for solvefor x,tan(2x)=-(((30+20)/2))/(80) is x=-(0.30288…)/2+(pin)/2

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solvefor x,tan(2x)=-(((30+20)/2))/(80)

solve for

x, tan (2 x) = - \frac{( \frac{30 + 20}{2} )}{80}

x = - \frac{0.30288 \dots}{2} + \frac{πn}{2}

Radians

x = - \frac{0.30288 \dots}{2} + \frac{π}{2} n

Solution steps

tan (2 x) = - \frac{( \frac{30 + 20}{2} )}{80}

Simplify

- \frac{\frac{30 + 20}{2}}{80} : - \frac{5}{16}

- \frac{\frac{30 + 20}{2}}{80}

Add the numbers:

30 + 20 = 50

= - \frac{\frac{50}{2}}{80}

Simplify

\frac{\frac{50}{2}}{80} : \frac{50}{160}

\frac{\frac{50}{2}}{80}

Apply the fraction rule:

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

= \frac{50}{2 \cdot 80}

Multiply the numbers:

2 \cdot 80 = 160

= \frac{50}{160}

= - \frac{50}{160}

Cancel the common factor:

10

= - \frac{5}{16}

Apply trig inverse properties

tan (2 x) = - \frac{5}{16}

General solutions for

tan (2 x) = - \frac{5}{16}

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

2 x = arctan (- \frac{5}{16}) + πn

2 x = arctan (- \frac{5}{16}) + πn

Solve

2 x = arctan (- \frac{5}{16}) + πn : x = - \frac{arctan ( \frac{5}{16} )}{2} + \frac{πn}{2}

2 x = arctan (- \frac{5}{16}) + πn

Simplify

arctan (- \frac{5}{16}) + πn : - arctan (\frac{5}{16}) + πn

arctan (- \frac{5}{16}) + πn

Use the following property:

arctan (- x) = - arctan (x)

arctan (- \frac{5}{16}) = - arctan (\frac{5}{16})

= - arctan (\frac{5}{16}) + πn

2 x = - arctan (\frac{5}{16}) + πn

Divide both sides by

2

2 x = - arctan (\frac{5}{16}) + πn

Divide both sides by

2

\frac{2 x}{2} = - \frac{arctan ( \frac{5}{16} )}{2} + \frac{πn}{2}

Simplify

x = - \frac{arctan ( \frac{5}{16} )}{2} + \frac{πn}{2}

x = - \frac{arctan ( \frac{5}{16} )}{2} + \frac{πn}{2}

x = - \frac{arctan ( \frac{5}{16} )}{2} + \frac{πn}{2}

Show solutions in decimal form

x = - \frac{0.30288 \dots}{2} + \frac{πn}{2}

4 cos (3 θ) = 2

sin (x) = - 0.8176

sin (x) = - 0.342

(cos (x) - 4) (cos (x) + 1) = 0

- 15 + 4 cos (x) = - 15 - 22

What is the general solution for solvefor x,tan(2x)=-(((30+20)/2))/(80) ?
The general solution for solvefor x,tan(2x)=-(((30+20)/2))/(80) is x=-(0.30288…)/2+(pin)/2