What is the general solution for tan(θ)=-(sqrt(7))/5 , pi/2 <θ<pi,cos(2θ) ?

The general solution for tan(θ)=-(sqrt(7))/5 , pi/2 <θ<pi,cos(2θ) is θ=-0.48669…+pi

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tan(θ)=-(sqrt(7))/5 , pi/2 <θ<pi,cos(2θ)

tan (θ) = - \frac{7}{5}, \frac{π}{2} < θ < π, cos (2 θ)

θ = - 0.48669 \dots + π

Degrees

θ = 152.11443 \dots^{\circ}

Solution steps

tan (θ) = - \frac{7}{5}, \frac{π}{2} < θ < π, cos (2 θ)

Apply trig inverse properties

tan (θ) = - \frac{7}{5}

General solutions for

tan (θ) = - \frac{7}{5}

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

θ = arctan (- \frac{7}{5}) + πn

θ = arctan (- \frac{7}{5}) + πn

Solutions for the range

\frac{π}{2} < θ < π

θ = - arctan (\frac{7}{5}) + π

Show solutions in decimal form

θ = - 0.48669 \dots + π

cos (θ) = - (\frac{1}{2})

cos (θ) = 2 cos (θ) - 1

2 cos^{2} (2 β) + cos (2 β) - 1 = 0, - 36 0^{\circ} \leq β \leq 36 0^{\circ}

cos (2 x) = \frac{3}{7}

0 = 1 - 3 cos (θ)

What is the general solution for tan(θ)=-(sqrt(7))/5 , pi/2 <θ<pi,cos(2θ) ?
The general solution for tan(θ)=-(sqrt(7))/5 , pi/2 <θ<pi,cos(2θ) is θ=-0.48669…+pi