What is the general solution for sin(θ)*csc(18)=1 ?

The general solution for sin(θ)*csc(18)=1 is θ=0.31415…+360n,θ=180-0.31415…+360n

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sin(θ)*csc(18)=1

sin (θ) \cdot csc (1 8^{\circ}) = 1

θ = 0.31415 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.31415 \dots + 36 0^{\circ} n

Solution steps

sin (θ) csc (1 8^{\circ}) = 1

csc (1 8^{\circ}) = \frac{2 ( 3 + 5 ) 3 - 5}{2}

sin (θ) \frac{2 ( 3 + 5 ) 3 - 5}{2} = 1

Multiply both sides by

2

2 (3 + 5) 3 - 5 sin (θ) = 2

Divide both sides by

2 (3 + 5) 3 - 5

sin (θ) = \frac{2 3 - 5}{4}

Apply trig inverse properties

θ = arcsin (\frac{2 3 - 5}{4}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{2 3 - 5}{4}) + 36 0^{\circ} n

Show solutions in decimal form

θ = 0.31415 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.31415 \dots + 36 0^{\circ} n

tan^{2} (x) + csc^{2} (x) = 3

x, y = arctan (x + y)

cos (x) = - sin^{2} (x) - 1, 0 \leq x \leq 2 π

θ, cos (θ) = \frac{- 1 2}{2}

cos^{2} (x) - sin (x) + 1 = 0

What is the general solution for sin(θ)*csc(18)=1 ?
The general solution for sin(θ)*csc(18)=1 is θ=0.31415…+360n,θ=180-0.31415…+360n