What is the general solution for sin(x)= 4/7 ?

The general solution for sin(x)= 4/7 is x=0.60824…+2pin,x=pi-0.60824…+2pin

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sin(x)= 4/7

sin (x) = \frac{4}{7}

x = 0.60824 \dots + 2 πn, x = π - 0.60824 \dots + 2 πn

Solution steps

sin (x) = \frac{4}{7}

Apply trig inverse properties

x = arcsin (\frac{4}{7}) + 2 πn, x = π - arcsin (\frac{4}{7}) + 2 πn

Show solutions in decimal form

x = 0.60824 \dots + 2 πn, x = π - 0.60824 \dots + 2 πn

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

4 sin (θ) + 5 = 3

(2 cos (x) + 3) (2 sin (x) + 1) = 0

sin^{2} (x) = 2 sin (x) + 3, 0 \leq x \leq 2 π

tan (x) = - 11

What is the general solution for sin(x)= 4/7 ?
The general solution for sin(x)= 4/7 is x=0.60824…+2pin,x=pi-0.60824…+2pin