What is the general solution for sin(x)= 5/7 ?

The general solution for sin(x)= 5/7 is x=0.79560…+2pin,x=pi-0.79560…+2pin

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sin(x)= 5/7

sin (x) = \frac{5}{7}

x = 0.79560 \dots + 2 πn, x = π - 0.79560 \dots + 2 πn

Degrees

x = 45.58469 \dots^{\circ} + 36 0^{\circ} n, x = 134.41530 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = \frac{5}{7}

Apply trig inverse properties

sin (x) = \frac{5}{7}

General solutions for

sin (x) = \frac{5}{7}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

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

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

Show solutions in decimal form

x = 0.79560 \dots + 2 πn, x = π - 0.79560 \dots + 2 πn

sec (t) = 2

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

2 tan^{2} (x) + 5 tan (x) + 3 = 0

csc^{2} (x) = 4

3 tanh (2 θ) = 5 sech (θ) + 1

What is the general solution for sin(x)= 5/7 ?
The general solution for sin(x)= 5/7 is x=0.79560…+2pin,x=pi-0.79560…+2pin