What is the general solution for sin(x)=0.2765 ?

The general solution for sin(x)=0.2765 is x=0.28015…+2pin,x=pi-0.28015…+2pin

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sin(x)=0.2765

sin (x) = 0.2765

x = 0.28015 \dots + 2 πn, x = π - 0.28015 \dots + 2 πn

Degrees

x = 16.05142 \dots^{\circ} + 36 0^{\circ} n, x = 163.94857 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = 0.2765

Apply trig inverse properties

sin (x) = 0.2765

General solutions for

sin (x) = 0.2765

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

x = arcsin (0.2765) + 2 πn, x = π - arcsin (0.2765) + 2 πn

x = arcsin (0.2765) + 2 πn, x = π - arcsin (0.2765) + 2 πn

Show solutions in decimal form

x = 0.28015 \dots + 2 πn, x = π - 0.28015 \dots + 2 πn

tan^{2} (x) = - \frac{3}{2} sec (x)

7 cos (θ) = 3 + cos (θ)

2 sin^{2} (x) - 9 sin (x) + 4 = 0

- 4 cos (θ) + 1 = 5

cos (2 x) = 0.4

What is the general solution for sin(x)=0.2765 ?
The general solution for sin(x)=0.2765 is x=0.28015…+2pin,x=pi-0.28015…+2pin