What is the general solution for sin(x)=(50*sin(145))/(120) ?

The general solution for sin(x)=(50*sin(145))/(120) is x=0.24132…+360n,x=180-0.24132…+360n

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sin(x)=(50*sin(145))/(120)

sin (x) = \frac{50 \cdot sin ( 14 5 ^{\circ} )}{120}

x = 0.24132 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.24132 \dots + 36 0^{\circ} n

Solution steps

sin (x) = \frac{50 sin ( 14 5 ^{\circ} )}{120}

Cancel the common factor:

10

sin (x) = \frac{5 sin ( 14 5 ^{\circ} )}{12}

Apply trig inverse properties

x = arcsin (\frac{5 sin ( 14 5 ^{\circ} )}{12}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{5 sin ( 14 5 ^{\circ} )}{12}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.24132 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.24132 \dots + 36 0^{\circ} n

cos^{2} (θ) - cos (θ) = sin^{2} (θ)

sin (x) + 2 sin^{2} (x) = 0

5 sec^{2} (x) - 5 = 0, 0 \leq x \leq 2 π

4 cos^{2} (θ) + 4 = 5

4 sin (2 z) - 3 cos (z) = 0

What is the general solution for sin(x)=(50*sin(145))/(120) ?
The general solution for sin(x)=(50*sin(145))/(120) is x=0.24132…+360n,x=180-0.24132…+360n