What is the general solution for tan(x/2)=-0.39 ?

The general solution for tan(x/2)=-0.39 is x=-2*0.37185…+2pin

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tan(x/2)=-0.39

tan (\frac{x}{2}) = - 0.39

x = - 2 \cdot 0.37185 \dots + 2 πn

Degrees

x = - 42.61156 \dots^{\circ} + 36 0^{\circ} n

Solution steps

tan (\frac{x}{2}) = - 0.39

Apply trig inverse properties

tan (\frac{x}{2}) = - 0.39

General solutions for

tan (\frac{x}{2}) = - 0.39

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

\frac{x}{2} = arctan (- 0.39) + πn

\frac{x}{2} = arctan (- 0.39) + πn

Solve

\frac{x}{2} = arctan (- 0.39) + πn : x = - 2 arctan (\frac{39}{100}) + 2 πn

\frac{x}{2} = arctan (- 0.39) + πn

Simplify

arctan (- 0.39) + πn : - arctan (\frac{39}{100}) + πn

arctan (- 0.39) + πn

arctan (- 0.39) = - arctan (\frac{39}{100})

arctan (- 0.39)

= arctan (- \frac{39}{100})

Use the following property:

arctan (- x) = - arctan (x)

arctan (- \frac{39}{100}) = - arctan (\frac{39}{100})

= - arctan (\frac{39}{100})

= - arctan (\frac{39}{100}) + πn

\frac{x}{2} = - arctan (\frac{39}{100}) + πn

Multiply both sides by

2

\frac{x}{2} = - arctan (\frac{39}{100}) + πn

Multiply both sides by

2

\frac{2 x}{2} = - 2 arctan (\frac{39}{100}) + 2 πn

Simplify

x = - 2 arctan (\frac{39}{100}) + 2 πn

x = - 2 arctan (\frac{39}{100}) + 2 πn

x = - 2 arctan (\frac{39}{100}) + 2 πn

Show solutions in decimal form

x = - 2 \cdot 0.37185 \dots + 2 πn

4 sin (3 x) - 1 = 0

3 tan (2 x - π) + 1 = 0

\frac{7}{4} cos (3 θ) - 1 = 0

cos (x) = sin (\frac{7 π}{6}), 0 \leq x \leq 2 π

cos (2 x) = \frac{( 3 k - 3 )}{8}

What is the general solution for tan(x/2)=-0.39 ?
The general solution for tan(x/2)=-0.39 is x=-2*0.37185…+2pin