What is the general solution for 2(19)tan(θ/2)=6.3 ?

The general solution for 2(19)tan(θ/2)=6.3 is θ=2*0.16429…+2pin

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2(19)tan(θ/2)=6.3

2 (19) tan (\frac{θ}{2}) = 6.3

θ = 2 \cdot 0.16429 \dots + 2 πn

Degrees

θ = 18.82682 \dots^{\circ} + 36 0^{\circ} n

Solution steps

2 (19) tan (\frac{θ}{2}) = 6.3

Divide both sides by

38

2 \cdot 19 tan (\frac{θ}{2}) = 6.3

Divide both sides by

38

\frac{2 \cdot 19 tan ( \frac{θ}{2} )}{38} = \frac{6.3}{38}

Simplify

tan (\frac{θ}{2}) = 0.16578 \dots

tan (\frac{θ}{2}) = 0.16578 \dots

Apply trig inverse properties

tan (\frac{θ}{2}) = 0.16578 \dots

General solutions for

tan (\frac{θ}{2}) = 0.16578 \dots

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

\frac{θ}{2} = arctan (0.16578 \dots) + πn

\frac{θ}{2} = arctan (0.16578 \dots) + πn

Solve

\frac{θ}{2} = arctan (0.16578 \dots) + πn : θ = 2 arctan (0.16578 \dots) + 2 πn

\frac{θ}{2} = arctan (0.16578 \dots) + πn

Multiply both sides by

2

\frac{θ}{2} = arctan (0.16578 \dots) + πn

Multiply both sides by

2

\frac{2 θ}{2} = 2 arctan (0.16578 \dots) + 2 πn

Simplify

θ = 2 arctan (0.16578 \dots) + 2 πn

θ = 2 arctan (0.16578 \dots) + 2 πn

θ = 2 arctan (0.16578 \dots) + 2 πn

Show solutions in decimal form

θ = 2 \cdot 0.16429 \dots + 2 πn

3 csc (x) - 6 = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

tan (\frac{x}{2} + \frac{π}{3}) = - 1

- sec^{2} (x) + 1 = - 5 sec (x) - 5

sec (t) = \frac{1}{- \frac{2}{2}}

sin (x) = 0.556692

What is the general solution for 2(19)tan(θ/2)=6.3 ?
The general solution for 2(19)tan(θ/2)=6.3 is θ=2*0.16429…+2pin