What is the general solution for sin(2x-10)= 3/7 ?

The general solution for sin(2x-10)= 3/7 is x=5+pin+(0.44291…)/2 ,x=pin+pi/2-(0.44291…)/2+5

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sin(2x-10)= 3/7

sin (2 x - 10) = \frac{3}{7}

x = 5 + πn + \frac{0.44291 \dots}{2}, x = πn + \frac{π}{2} - \frac{0.44291 \dots}{2} + 5

Solution steps

sin (2 x - 10) = \frac{3}{7}

Apply trig inverse properties

2 x - 10 = arcsin (\frac{3}{7}) + 2 πn, 2 x - 10 = π - arcsin (\frac{3}{7}) + 2 πn

Solve

2 x - 10 = arcsin (\frac{3}{7}) + 2 πn : x = 5 + πn + \frac{arcsin ( \frac{3}{7} )}{2}

Solve

2 x - 10 = π - arcsin (\frac{3}{7}) + 2 πn : x = πn + \frac{π}{2} - \frac{arcsin ( \frac{3}{7} )}{2} + 5

x = 5 + πn + \frac{arcsin ( \frac{3}{7} )}{2}, x = πn + \frac{π}{2} - \frac{arcsin ( \frac{3}{7} )}{2} + 5

Show solutions in decimal form

x = 5 + πn + \frac{0.44291 \dots}{2}, x = πn + \frac{π}{2} - \frac{0.44291 \dots}{2} + 5

2 cos^{2} (θ) + 3 sin (θ) = 3

sin (5 x) + sin (3 x) = 0

sin (θ) = \frac{1}{7}

2 cos^{2} (x) - 5 cos (x) = 3

4 arctan (x) = π

What is the general solution for sin(2x-10)= 3/7 ?
The general solution for sin(2x-10)= 3/7 is x=5+pin+(0.44291…)/2 ,x=pin+pi/2-(0.44291…)/2+5