What is the general solution for tan(2θ)=(73-8)/(-10) ?

The general solution for tan(2θ)=(73-8)/(-10) is θ=-(1.41814…)/2+(pin)/2

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tan(2θ)=(73-8)/(-10)

tan (2 θ) = \frac{73 - 8}{- 10}

θ = - \frac{1.41814 \dots}{2} + \frac{πn}{2}

Radians

θ = - \frac{1.41814 \dots}{2} + \frac{π}{2} n

Solution steps

tan (2 θ) = \frac{73 - 8}{- 10}

Simplify

\frac{73 - 8}{- 10} : - \frac{13}{2}

\frac{73 - 8}{- 10}

Subtract the numbers:

73 - 8 = 65

= \frac{65}{- 10}

Apply the fraction rule:

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

= - \frac{65}{10}

Cancel the common factor:

5

= - \frac{13}{2}

Apply trig inverse properties

tan (2 θ) = - \frac{13}{2}

General solutions for

tan (2 θ) = - \frac{13}{2}

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

2 θ = arctan (- \frac{13}{2}) + πn

2 θ = arctan (- \frac{13}{2}) + πn

Solve

2 θ = arctan (- \frac{13}{2}) + πn : θ = - \frac{arctan ( \frac{13}{2} )}{2} + \frac{πn}{2}

2 θ = arctan (- \frac{13}{2}) + πn

Simplify

arctan (- \frac{13}{2}) + πn : - arctan (\frac{13}{2}) + πn

arctan (- \frac{13}{2}) + πn

Use the following property:

arctan (- x) = - arctan (x)

arctan (- \frac{13}{2}) = - arctan (\frac{13}{2})

= - arctan (\frac{13}{2}) + πn

2 θ = - arctan (\frac{13}{2}) + πn

Divide both sides by

2

2 θ = - arctan (\frac{13}{2}) + πn

Divide both sides by

2

\frac{2 θ}{2} = - \frac{arctan ( \frac{13}{2} )}{2} + \frac{πn}{2}

Simplify

θ = - \frac{arctan ( \frac{13}{2} )}{2} + \frac{πn}{2}

θ = - \frac{arctan ( \frac{13}{2} )}{2} + \frac{πn}{2}

θ = - \frac{arctan ( \frac{13}{2} )}{2} + \frac{πn}{2}

Show solutions in decimal form

θ = - \frac{1.41814 \dots}{2} + \frac{πn}{2}

x, T (7) = 3.15 cos (\frac{π}{6} x) + 19.15

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

\frac{( ( sin ( x ) ) )}{( a )} = k

sin (θ) = \frac{2}{2}, 0 \leq θ < 2 π

x, 10 (cos (x))^{2} + 5 cos (x) - 5 = 0

What is the general solution for tan(2θ)=(73-8)/(-10) ?
The general solution for tan(2θ)=(73-8)/(-10) is θ=-(1.41814…)/2+(pin)/2