What is the general solution for tan(2x)=-0.5 ?

The general solution for tan(2x)=-0.5 is x=-(0.46364…)/2+(pin)/2

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tan(2x)=-0.5

tan (2 x) = - 0.5

x = - \frac{0.46364 \dots}{2} + \frac{πn}{2}

Degrees

x = - 13.28252 \dots^{\circ} + 9 0^{\circ} n

Solution steps

tan (2 x) = - 0.5

Apply trig inverse properties

tan (2 x) = - 0.5

General solutions for

tan (2 x) = - 0.5

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

2 x = arctan (- 0.5) + πn

2 x = arctan (- 0.5) + πn

Solve

2 x = arctan (- 0.5) + πn : x = - \frac{arctan ( \frac{1}{2} )}{2} + \frac{πn}{2}

2 x = arctan (- 0.5) + πn

Simplify

arctan (- 0.5) + πn : - arctan (\frac{1}{2}) + πn

arctan (- 0.5) + πn

arctan (- 0.5) = - arctan (\frac{1}{2})

arctan (- 0.5)

= arctan (- \frac{1}{2})

Use the following property:

arctan (- x) = - arctan (x)

arctan (- \frac{1}{2}) = - arctan (\frac{1}{2})

= - arctan (\frac{1}{2})

= - arctan (\frac{1}{2}) + πn

2 x = - arctan (\frac{1}{2}) + πn

Divide both sides by

2

2 x = - arctan (\frac{1}{2}) + πn

Divide both sides by

2

\frac{2 x}{2} = - \frac{arctan ( \frac{1}{2} )}{2} + \frac{πn}{2}

Simplify

x = - \frac{arctan ( \frac{1}{2} )}{2} + \frac{πn}{2}

x = - \frac{arctan ( \frac{1}{2} )}{2} + \frac{πn}{2}

x = - \frac{arctan ( \frac{1}{2} )}{2} + \frac{πn}{2}

Show solutions in decimal form

x = - \frac{0.46364 \dots}{2} + \frac{πn}{2}

2 sin^{2} (x) + cos (x) - 1 = 0, in t er v a l^{0}, 2 π

tan (x) = \frac{100}{23}

4 sin (\frac{x}{2}) + 4 cos (x) = 0

cos (θ) cos (θ) = cot (θ)

3 sin (θ) - cos (2 θ) = 1

What is the general solution for tan(2x)=-0.5 ?
The general solution for tan(2x)=-0.5 is x=-(0.46364…)/2+(pin)/2