What is the general solution for tan(2x)=-40/3 ?

The general solution for tan(2x)=-40/3 is x=-(1.49593…)/2+(pin)/2

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tan(2x)=-40/3

tan (2 x) = - \frac{40}{3}

x = - \frac{1.49593 \dots}{2} + \frac{πn}{2}

Solution steps

tan (2 x) = - \frac{40}{3}

Apply trig inverse properties

2 x = arctan (- \frac{40}{3}) + πn

Solve

2 x = arctan (- \frac{40}{3}) + πn : x = - \frac{arctan ( \frac{40}{3} )}{2} + \frac{πn}{2}

x = - \frac{arctan ( \frac{40}{3} )}{2} + \frac{πn}{2}

Show solutions in decimal form

x = - \frac{1.49593 \dots}{2} + \frac{πn}{2}

3 cos (2 x) - 5 sin (x) + 1 = 0

tan (θ) = \frac{5}{- 2}

sin (x + \frac{π}{2}) = \frac{1}{2}

8 cos (x) + 4 = 0

6 = 6 (1 - sin (θ))

What is the general solution for tan(2x)=-40/3 ?
The general solution for tan(2x)=-40/3 is x=-(1.49593…)/2+(pin)/2