What is the general solution for sin(x)=0.75 ?

The general solution for sin(x)=0.75 is x=0.84806…+2pin,x=pi-0.84806…+2pin

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sin(x)=0.75

sin (x) = 0.75

x = 0.84806 \dots + 2 πn, x = π - 0.84806 \dots + 2 πn

Degrees

x = 48.59037 \dots^{\circ} + 36 0^{\circ} n, x = 131.40962 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = 0.75

Apply trig inverse properties

sin (x) = 0.75

General solutions for

sin (x) = 0.75

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

x = arcsin (0.75) + 2 πn, x = π - arcsin (0.75) + 2 πn

x = arcsin (0.75) + 2 πn, x = π - arcsin (0.75) + 2 πn

Show solutions in decimal form

x = 0.84806 \dots + 2 πn, x = π - 0.84806 \dots + 2 πn

(cot (θ) - 1) (csc (θ) + 1) = 0

tan (θ) = - \frac{2}{3}

cot^{2} (x) = csc (x) - 1

sin (θ) = - \frac{2}{3}

50 sin^{2} (x) = 50 + 25 cos (x)

What is the general solution for sin(x)=0.75 ?
The general solution for sin(x)=0.75 is x=0.84806…+2pin,x=pi-0.84806…+2pin