What is the general solution for sin(x)=sin(80) ?

The general solution for sin(x)=sin(80) is x=1.39626…+360n,x=180-1.39626…+360n

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sin(x)=sin(80)

sin (x) = sin (8 0^{\circ})

x = 1.39626 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.39626 \dots + 36 0^{\circ} n

Radians

x = 1.39626 \dots + 2 πn, x = π - 1.39626 \dots + 2 πn

Solution steps

sin (x) = sin (8 0^{\circ})

Apply trig inverse properties

sin (x) = sin (8 0^{\circ})

General solutions for

sin (x) = sin (8 0^{\circ})

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

x = arcsin (sin (8 0^{\circ})) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (sin (8 0^{\circ})) + 36 0^{\circ} n

x = arcsin (sin (8 0^{\circ})) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (sin (8 0^{\circ})) + 36 0^{\circ} n

Show solutions in decimal form

x = 1.39626 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.39626 \dots + 36 0^{\circ} n

tan (A) = 2.0503

cot (x) = - 3, 0 \leq x \leq 2 π

2 sin (4 x) - 1 = 0

cot (θ) = 0.75

6 sin (x) - 2 cos (x) = 2

What is the general solution for sin(x)=sin(80) ?
The general solution for sin(x)=sin(80) is x=1.39626…+360n,x=180-1.39626…+360n