What is the general solution for sin(θ)=(7sin(140))/(16.12288984) ?

The general solution for sin(θ)=(7sin(140))/(16.12288984) is θ=0.28283…+360n,θ=180-0.28283…+360n

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sin(θ)=(7sin(140))/(16.12288984)

sin (θ) = \frac{7 sin ( 14 0 ^{\circ} )}{16.12288984}

θ = 0.28283 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.28283 \dots + 36 0^{\circ} n

Radians

θ = 0.28283 \dots + 2 πn, θ = π - 0.28283 \dots + 2 πn

Solution steps

sin (θ) = \frac{7 sin ( 14 0 ^{\circ} )}{16.12288 \dots}

Apply trig inverse properties

sin (θ) = \frac{7 sin ( 14 0 ^{\circ} )}{16.12288 \dots}

General solutions for

sin (θ) = \frac{7 sin ( 14 0 ^{\circ} )}{16.12288 \dots}

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

θ = arcsin (\frac{7 sin ( 14 0 ^{\circ} )}{16.12288 \dots}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{7 sin ( 14 0 ^{\circ} )}{16.12288 \dots}) + 36 0^{\circ} n

θ = arcsin (\frac{7 sin ( 14 0 ^{\circ} )}{16.12288 \dots}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{7 sin ( 14 0 ^{\circ} )}{16.12288 \dots}) + 36 0^{\circ} n

Show solutions in decimal form

θ = 0.28283 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.28283 \dots + 36 0^{\circ} n

- 5 cos^{2} (x) = 0

tan (2 x) + sec (2 x) = 5

tan (2 x) + sec (2 x) = 1

cos^{2} (x) = \frac{( 4 k - 5 )}{10}

csc (A) = 3

What is the general solution for sin(θ)=(7sin(140))/(16.12288984) ?
The general solution for sin(θ)=(7sin(140))/(16.12288984) is θ=0.28283…+360n,θ=180-0.28283…+360n