What is the general solution for tan(2θ)=(500)/(350-75) ?

The general solution for tan(2θ)=(500)/(350-75) is θ=(1.06795…)/2+(pin)/2

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tan(2θ)=(500)/(350-75)

tan (2 θ) = \frac{500}{350 - 75}

θ = \frac{1.06795 \dots}{2} + \frac{πn}{2}

Radians

θ = \frac{1.06795 \dots}{2} + \frac{π}{2} n

Solution steps

tan (2 θ) = \frac{500}{350 - 75}

Simplify

\frac{500}{350 - 75} : \frac{20}{11}

\frac{500}{350 - 75}

Subtract the numbers:

350 - 75 = 275

= \frac{500}{275}

Cancel the common factor:

25

= \frac{20}{11}

Apply trig inverse properties

tan (2 θ) = \frac{20}{11}

General solutions for

tan (2 θ) = \frac{20}{11}

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

2 θ = arctan (\frac{20}{11}) + πn

2 θ = arctan (\frac{20}{11}) + πn

Solve

2 θ = arctan (\frac{20}{11}) + πn : θ = \frac{arctan ( \frac{20}{11} )}{2} + \frac{πn}{2}

2 θ = arctan (\frac{20}{11}) + πn

Divide both sides by

2

2 θ = arctan (\frac{20}{11}) + πn

Divide both sides by

2

\frac{2 θ}{2} = \frac{arctan ( \frac{20}{11} )}{2} + \frac{πn}{2}

Simplify

θ = \frac{arctan ( \frac{20}{11} )}{2} + \frac{πn}{2}

θ = \frac{arctan ( \frac{20}{11} )}{2} + \frac{πn}{2}

θ = \frac{arctan ( \frac{20}{11} )}{2} + \frac{πn}{2}

Show solutions in decimal form

θ = \frac{1.06795 \dots}{2} + \frac{πn}{2}

sec (a) = - 2

tan^{2} (γ) + 1 = cos^{2} (γ)

sin^{2} (x) + 8 sin (x) - 9 = 0

- 2 sin^{2} (θ) + 10 sin (θ) - 3 = 3 sin (θ), 0^{\circ} \leq θ < 36 0^{\circ}

cot^{2} (θ) + 4 csc (θ) = - 5

What is the general solution for tan(2θ)=(500)/(350-75) ?
The general solution for tan(2θ)=(500)/(350-75) is θ=(1.06795…)/2+(pin)/2