What is the general solution for tan(2θ)=-1.75 ?

The general solution for tan(2θ)=-1.75 is θ=-(1.05165…)/2+(pin)/2

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tan(2θ)=-1.75

tan (2 θ) = - 1.75

θ = - \frac{1.05165 \dots}{2} + \frac{πn}{2}

Degrees

θ = - 30.12755 \dots^{\circ} + 9 0^{\circ} n

Solution steps

tan (2 θ) = - 1.75

Apply trig inverse properties

tan (2 θ) = - 1.75

General solutions for

tan (2 θ) = - 1.75

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

2 θ = arctan (- 1.75) + πn

2 θ = arctan (- 1.75) + πn

Solve

2 θ = arctan (- 1.75) + πn : θ = - \frac{arctan ( \frac{7}{4} )}{2} + \frac{πn}{2}

2 θ = arctan (- 1.75) + πn

Simplify

arctan (- 1.75) + πn : - arctan (\frac{7}{4}) + πn

arctan (- 1.75) + πn

arctan (- 1.75) = - arctan (\frac{7}{4})

arctan (- 1.75)

= arctan (- \frac{7}{4})

Use the following property:

arctan (- x) = - arctan (x)

arctan (- \frac{7}{4}) = - arctan (\frac{7}{4})

= - arctan (\frac{7}{4})

= - arctan (\frac{7}{4}) + πn

2 θ = - arctan (\frac{7}{4}) + πn

Divide both sides by

2

2 θ = - arctan (\frac{7}{4}) + πn

Divide both sides by

2

\frac{2 θ}{2} = - \frac{arctan ( \frac{7}{4} )}{2} + \frac{πn}{2}

Simplify

θ = - \frac{arctan ( \frac{7}{4} )}{2} + \frac{πn}{2}

θ = - \frac{arctan ( \frac{7}{4} )}{2} + \frac{πn}{2}

θ = - \frac{arctan ( \frac{7}{4} )}{2} + \frac{πn}{2}

Show solutions in decimal form

θ = - \frac{1.05165 \dots}{2} + \frac{πn}{2}

cos (x) = \frac{3}{2}, tan (x)

tan (t) = \frac{7}{24}

cos (x) = 0.59

cos (x) = 0.92

cos (x) = 0.94

What is the general solution for tan(2θ)=-1.75 ?
The general solution for tan(2θ)=-1.75 is θ=-(1.05165…)/2+(pin)/2