What is the general solution for 250sin(75)=393.19sin(45-θ) ?

The general solution for 250sin(75)=393.19sin(45-θ) is θ=-360n+45-0.66132…,θ=-180-360n+45+0.66132…

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250sin(75)=393.19sin(45-θ)

250 sin (7 5^{\circ}) = 393.19 sin (4 5^{\circ} - θ)

θ = - 36 0^{\circ} n + 4 5^{\circ} - 0.66132 \dots, θ = - 18 0^{\circ} - 36 0^{\circ} n + 4 5^{\circ} + 0.66132 \dots

Solution steps

250 sin (7 5^{\circ}) = 393.19 sin (4 5^{\circ} - θ)

sin (7 5^{\circ}) = \frac{6 + 2}{4}

250 \cdot \frac{6 + 2}{4} = 393.19 sin (4 5^{\circ} - θ)

Switch sides

393.19 sin (4 5^{\circ} - θ) = 250 \cdot \frac{6 + 2}{4}

Multiply both sides by

100

39319 sin (4 5^{\circ} - θ) = 6250 (6 + 2)

Divide both sides by

39319

sin (4 5^{\circ} - θ) = \frac{6250 ( 6 + 2 )}{39319}

Apply trig inverse properties

4 5^{\circ} - θ = arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n, 4 5^{\circ} - θ = 18 0^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n

Solve

4 5^{\circ} - θ = arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n : θ = - 36 0^{\circ} n + 4 5^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319})

Solve

4 5^{\circ} - θ = 18 0^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319}) + 36 0^{\circ} n : θ = - 18 0^{\circ} - 36 0^{\circ} n + 4 5^{\circ} + arcsin (\frac{6250 ( 6 + 2 )}{39319})

θ = - 36 0^{\circ} n + 4 5^{\circ} - arcsin (\frac{6250 ( 6 + 2 )}{39319}), θ = - 18 0^{\circ} - 36 0^{\circ} n + 4 5^{\circ} + arcsin (\frac{6250 ( 6 + 2 )}{39319})

Show solutions in decimal form

θ = - 36 0^{\circ} n + 4 5^{\circ} - 0.66132 \dots, θ = - 18 0^{\circ} - 36 0^{\circ} n + 4 5^{\circ} + 0.66132 \dots

tan (θ) = \frac{6}{6.71}

x, sin (x) - 1 = 0

sin^{2} (θ) = 1 + cos (2 θ)

4 sin^{2} (θ) = 3 - 2 sin^{2} (θ)

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

What is the general solution for 250sin(75)=393.19sin(45-θ) ?
The general solution for 250sin(75)=393.19sin(45-θ) is θ=-360n+45-0.66132…,θ=-180-360n+45+0.66132…