What is the general solution for tan(2β)=-4/3 ?

The general solution for tan(2β)=-4/3 is β=-(0.92729…)/2+(pin)/2

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tan(2β)=-4/3

tan (2 β) = - \frac{4}{3}

β = - \frac{0.92729 \dots}{2} + \frac{πn}{2}

Degrees

β = - 26.56505 \dots^{\circ} + 9 0^{\circ} n

Solution steps

tan (2 β) = - \frac{4}{3}

Apply trig inverse properties

tan (2 β) = - \frac{4}{3}

General solutions for

tan (2 β) = - \frac{4}{3}

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

2 β = arctan (- \frac{4}{3}) + πn

2 β = arctan (- \frac{4}{3}) + πn

Solve

2 β = arctan (- \frac{4}{3}) + πn : β = - \frac{arctan ( \frac{4}{3} )}{2} + \frac{πn}{2}

2 β = arctan (- \frac{4}{3}) + πn

Simplify

arctan (- \frac{4}{3}) + πn : - arctan (\frac{4}{3}) + πn

arctan (- \frac{4}{3}) + πn

Use the following property:

arctan (- x) = - arctan (x)

arctan (- \frac{4}{3}) = - arctan (\frac{4}{3})

= - arctan (\frac{4}{3}) + πn

2 β = - arctan (\frac{4}{3}) + πn

Divide both sides by

2

2 β = - arctan (\frac{4}{3}) + πn

Divide both sides by

2

\frac{2 β}{2} = - \frac{arctan ( \frac{4}{3} )}{2} + \frac{πn}{2}

Simplify

β = - \frac{arctan ( \frac{4}{3} )}{2} + \frac{πn}{2}

β = - \frac{arctan ( \frac{4}{3} )}{2} + \frac{πn}{2}

β = - \frac{arctan ( \frac{4}{3} )}{2} + \frac{πn}{2}

Show solutions in decimal form

β = - \frac{0.92729 \dots}{2} + \frac{πn}{2}

4 cos^{2} (x) - 5 cos (x) - 6 = 0

3 sec^{2} (\frac{x}{2}) - 4 sec (\frac{x}{2}) - 4 = 0

tan (x) = \frac{3}{10 cos ( x )}, 0^{\circ} < x < 9 0^{\circ}

2 cos^{2} (x) - 3 cos (x) = 0, 0, 2 π

2 cos^{2} (x) - 5 sin (x) = 4

What is the general solution for tan(2β)=-4/3 ?
The general solution for tan(2β)=-4/3 is β=-(0.92729…)/2+(pin)/2