What is the general solution for sin(x)=0.7 ?

The general solution for sin(x)=0.7 is x=0.77539…+2pin,x=pi-0.77539…+2pin

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sin(x)=0.7

sin (x) = 0.7

x = 0.77539 \dots + 2 πn, x = π - 0.77539 \dots + 2 πn

Solution steps

sin (x) = 0.7

Apply trig inverse properties

x = arcsin (0.7) + 2 πn, x = π - arcsin (0.7) + 2 πn

Show solutions in decimal form

x = 0.77539 \dots + 2 πn, x = π - 0.77539 \dots + 2 πn

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

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

sec (θ) = 2

2 cos^{2} (θ) - 3 cos (θ) + 1 = 0

cos (2 θ) = 1

What is the general solution for sin(x)=0.7 ?
The general solution for sin(x)=0.7 is x=0.77539…+2pin,x=pi-0.77539…+2pin