What is the general solution for sin(x)=0.7547 ?

The general solution for sin(x)=0.7547 is x=0.85519…+2pin,x=pi-0.85519…+2pin

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sin(x)=0.7547

sin (x) = 0.7547

x = 0.85519 \dots + 2 πn, x = π - 0.85519 \dots + 2 πn

Degrees

x = 48.99916 \dots^{\circ} + 36 0^{\circ} n, x = 131.00083 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = 0.7547

Apply trig inverse properties

sin (x) = 0.7547

General solutions for

sin (x) = 0.7547

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

x = arcsin (0.7547) + 2 πn, x = π - arcsin (0.7547) + 2 πn

x = arcsin (0.7547) + 2 πn, x = π - arcsin (0.7547) + 2 πn

Show solutions in decimal form

x = 0.85519 \dots + 2 πn, x = π - 0.85519 \dots + 2 πn

cos (2 x - \frac{π}{6}) = \frac{( 3 )}{2}, 0 < x < 2 π

- 1 = tan (x)

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

2 tan (x) = 1 - tan^{2} (x)

3 sin (θ) + 3 = 2 cos^{2} (θ)

What is the general solution for sin(x)=0.7547 ?
The general solution for sin(x)=0.7547 is x=0.85519…+2pin,x=pi-0.85519…+2pin