What is the general solution for sin(x)=(150)/(212.6)(sin(115)) ?

The general solution for sin(x)=(150)/(212.6)(sin(115)) is x=0.69377…+360n,x=180-0.69377…+360n

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sin(x)=(150)/(212.6)(sin(115))

sin (x) = \frac{150}{212.6} (sin (11 5^{\circ}))

x = 0.69377 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.69377 \dots + 36 0^{\circ} n

Radians

x = 0.69377 \dots + 2 πn, x = π - 0.69377 \dots + 2 πn

Solution steps

sin (x) = \frac{150}{212.6} (sin (11 5^{\circ}))

Apply trig inverse properties

sin (x) = \frac{150}{212.6} sin (11 5^{\circ})

General solutions for

sin (x) = \frac{150}{212.6} sin (11 5^{\circ})

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

x = arcsin (\frac{150}{212.6} sin (11 5^{\circ})) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{150}{212.6} sin (11 5^{\circ})) + 36 0^{\circ} n

x = arcsin (\frac{150}{212.6} sin (11 5^{\circ})) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{150}{212.6} sin (11 5^{\circ})) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.69377 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.69377 \dots + 36 0^{\circ} n

16 cos (2 θ) - 9 = 0

0 = 2 + 3 cos (θ) + cos (2 θ)

sin (2 θ) = cos (θ), 2

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

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

What is the general solution for sin(x)=(150)/(212.6)(sin(115)) ?
The general solution for sin(x)=(150)/(212.6)(sin(115)) is x=0.69377…+360n,x=180-0.69377…+360n