What is the general solution for sin(b)=0.775 ?

The general solution for sin(b)=0.775 is b=0.88671…+2pin,b=pi-0.88671…+2pin

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sin(b)=0.775

sin (b) = 0.775

b = 0.88671 \dots + 2 πn, b = π - 0.88671 \dots + 2 πn

Degrees

b = 50.80503 \dots^{\circ} + 36 0^{\circ} n, b = 129.19496 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (b) = 0.775

Apply trig inverse properties

sin (b) = 0.775

General solutions for

sin (b) = 0.775

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

b = arcsin (0.775) + 2 πn, b = π - arcsin (0.775) + 2 πn

b = arcsin (0.775) + 2 πn, b = π - arcsin (0.775) + 2 πn

Show solutions in decimal form

b = 0.88671 \dots + 2 πn, b = π - 0.88671 \dots + 2 πn

- 2 cos^{2} (x) + 3 sin (x) + 3 = 0

2 cos^{2} (x) = 3 \cdot cos (x)

4 (cos (x) + 1) cos (x) = 3

sin^{2} (x) + 1 = cos^{2} (x) - 2 sin^{4} (x)

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

What is the general solution for sin(b)=0.775 ?
The general solution for sin(b)=0.775 is b=0.88671…+2pin,b=pi-0.88671…+2pin