What is the general solution for sin(θ)=(10sin(105))/(24.6) ?

The general solution for sin(θ)=(10sin(105))/(24.6) is θ=0.40351…+360n,θ=180-0.40351…+360n

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sin(θ)=(10sin(105))/(24.6)

sin (θ) = \frac{10 sin ( 10 5 ^{\circ} )}{24.6}

θ = 0.40351 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.40351 \dots + 36 0^{\circ} n

Solution steps

sin (θ) = \frac{10 sin ( 10 5 ^{\circ} )}{24.6}

sin (10 5^{\circ}) = \frac{2 ( 3 + 1 )}{4}

sin (θ) = \frac{10 \cdot \frac{2 ( 3 + 1 )}{4}}{24.6}

Simplify

\frac{10 \cdot \frac{2 ( 3 + 1 )}{4}}{24.6} : \frac{5 2 ( 3 + 1 )}{49.2}

Apply trig inverse properties

θ = arcsin (\frac{5 2 ( 3 + 1 )}{49.2}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{5 2 ( 3 + 1 )}{49.2}) + 36 0^{\circ} n

Show solutions in decimal form

θ = 0.40351 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.40351 \dots + 36 0^{\circ} n

0.175 = 0.34 sin (93.4 x)

2 - cos^{2} (x) + 3 sin (x) + 1 = cos^{2} (x)

cos (B) = 2425, tan (B)

1 - tan^{4} (a) cos^{4} (a) = 1 - 2 sin^{2} (a)

cos (0.5 x) = 0.5, - π \leq x \leq π

What is the general solution for sin(θ)=(10sin(105))/(24.6) ?
The general solution for sin(θ)=(10sin(105))/(24.6) is θ=0.40351…+360n,θ=180-0.40351…+360n