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

Radians

x = 0.24132 \dots + 2 πn, x = π - 0.24132 \dots + 2 πn

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

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

General solutions for

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

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

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

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

0.34 = cos (x)

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

x, 2 y sin (x) = 0

- 14 sin (x) + 14 cos (2 x) = 0

sin (x) = \frac{10}{25}

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