What is the general solution for tan(3.87x)=-0.78 ?

The general solution for tan(3.87x)=-0.78 is x=-(0.66242…)/(3.87)+(pin)/(3.87)

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tan(3.87x)=-0.78

tan (3.87 x) = - 0.78

x = - \frac{0.66242 \dots}{3.87} + \frac{πn}{3.87}

Degrees

x = - 9.80729 \dots^{\circ} + 46.51162 \dots^{\circ} n

Solution steps

tan (3.87 x) = - 0.78

Apply trig inverse properties

tan (3.87 x) = - 0.78

General solutions for

tan (3.87 x) = - 0.78

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

3.87 x = arctan (- 0.78) + πn

3.87 x = arctan (- 0.78) + πn

Solve

3.87 x = arctan (- 0.78) + πn : x = - \frac{arctan ( \frac{39}{50} )}{3.87} + \frac{πn}{3.87}

3.87 x = arctan (- 0.78) + πn

Simplify

arctan (- 0.78) + πn : - arctan (\frac{39}{50}) + πn

arctan (- 0.78) + πn

arctan (- 0.78) = - arctan (\frac{39}{50})

arctan (- 0.78)

= arctan (- \frac{39}{50})

Use the following property:

arctan (- x) = - arctan (x)

arctan (- \frac{39}{50}) = - arctan (\frac{39}{50})

= - arctan (\frac{39}{50})

= - arctan (\frac{39}{50}) + πn

3.87 x = - arctan (\frac{39}{50}) + πn

Divide both sides by

3.87

3.87 x = - arctan (\frac{39}{50}) + πn

Divide both sides by

3.87

\frac{3.87 x}{3.87} = - \frac{arctan ( \frac{39}{50} )}{3.87} + \frac{πn}{3.87}

Simplify

x = - \frac{arctan ( \frac{39}{50} )}{3.87} + \frac{πn}{3.87}

x = - \frac{arctan ( \frac{39}{50} )}{3.87} + \frac{πn}{3.87}

x = - \frac{arctan ( \frac{39}{50} )}{3.87} + \frac{πn}{3.87}

Show solutions in decimal form

x = - \frac{0.66242 \dots}{3.87} + \frac{πn}{3.87}

sin (2 x) = \frac{( 2 m - 4 )}{5}

34 sin (\frac{π}{6} (x - 43)) = 34

3 sin (3 x) = 2

2 sinh (2 x) - 6 cosh (x) = 0

- cos (x) = - 1

What is the general solution for tan(3.87x)=-0.78 ?
The general solution for tan(3.87x)=-0.78 is x=-(0.66242…)/(3.87)+(pin)/(3.87)