What is the general solution for tan(3x-4)=(-1)/2 ?

The general solution for tan(3x-4)=(-1)/2 is x=-(0.46364…)/3+(pin)/3+4/3

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tan(3x-4)=(-1)/2

tan (3 x - 4) = \frac{- 1}{2}

x = - \frac{0.46364 \dots}{3} + \frac{πn}{3} + \frac{4}{3}

Solution steps

tan (3 x - 4) = \frac{- 1}{2}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

tan (3 x - 4) = - \frac{1}{2}

Apply trig inverse properties

3 x - 4 = arctan (- \frac{1}{2}) + πn

Solve

3 x - 4 = arctan (- \frac{1}{2}) + πn : x = - \frac{arctan ( \frac{1}{2} )}{3} + \frac{πn}{3} + \frac{4}{3}

x = - \frac{arctan ( \frac{1}{2} )}{3} + \frac{πn}{3} + \frac{4}{3}

Show solutions in decimal form

x = - \frac{0.46364 \dots}{3} + \frac{πn}{3} + \frac{4}{3}

π cos (2 θ) = 0

2 + 3 sec (x) - 4 cos (x) = 23

4 sin (x) \cdot cos (x) = 2 sin (x)

- 1 sec^{2} (θ) + 2 sec (θ) = 1

cos (θ) = 0.8701

What is the general solution for tan(3x-4)=(-1)/2 ?
The general solution for tan(3x-4)=(-1)/2 is x=-(0.46364…)/3+(pin)/3+4/3