What is the general solution for tan(θ/3)=3sin(48) ?

The general solution for tan(θ/3)=3sin(48) is θ=3*1.14915…+540n

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tan(θ/3)=3sin(48)

tan (\frac{θ}{3}) = 3 sin (4 8^{\circ})

θ = 3 \cdot 1.14915 \dots + 54 0^{\circ} n

Radians

θ = 3 \cdot 1.14915 \dots + 3 πn

Solution steps

tan (\frac{θ}{3}) = 3 sin (4 8^{\circ})

Apply trig inverse properties

tan (\frac{θ}{3}) = 3 sin (4 8^{\circ})

General solutions for

tan (\frac{θ}{3}) = 3 sin (4 8^{\circ})

tan (x) = a \Rightarrow x = arctan (a) + 18 0^{\circ} n

\frac{θ}{3} = arctan (3 sin (4 8^{\circ})) + 18 0^{\circ} n

\frac{θ}{3} = arctan (3 sin (4 8^{\circ})) + 18 0^{\circ} n

Solve

\frac{θ}{3} = arctan (3 sin (4 8^{\circ})) + 18 0^{\circ} n : θ = 3 arctan (3 sin (4 8^{\circ})) + 54 0^{\circ} n

\frac{θ}{3} = arctan (3 sin (4 8^{\circ})) + 18 0^{\circ} n

Multiply both sides by

3

\frac{θ}{3} = arctan (3 sin (4 8^{\circ})) + 18 0^{\circ} n

Multiply both sides by

3

\frac{3 θ}{3} = 3 arctan (3 sin (4 8^{\circ})) + 54 0^{\circ} n

Simplify

θ = 3 arctan (3 sin (4 8^{\circ})) + 54 0^{\circ} n

θ = 3 arctan (3 sin (4 8^{\circ})) + 54 0^{\circ} n

θ = 3 arctan (3 sin (4 8^{\circ})) + 54 0^{\circ} n

Show solutions in decimal form

θ = 3 \cdot 1.14915 \dots + 54 0^{\circ} n

\frac{cos ( x ) cot ( x )}{1 - sin ( x )} = csc (x)

2 cos^{2} (x) - 9 sin (x) - 3 = 0

3 + \frac{1}{5} \cdot cos (\frac{θ}{3} + \frac{7 π}{4}) = 3

cosh (2 x) = 2 cosh (x) - 1

1 = \frac{3 sin ^{2} ( x )}{cos ^{2} ( x )}

What is the general solution for tan(θ/3)=3sin(48) ?
The general solution for tan(θ/3)=3sin(48) is θ=3*1.14915…+540n