What is the general solution for csc(x+10)=3 ?

The general solution for csc(x+10)=3 is x=0.33983…+360n-10,x=180-0.33983…+360n-10

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csc(x+10)=3

csc (x + 1 0^{\circ}) = 3

x = 0.33983 \dots + 36 0^{\circ} n - 1 0^{\circ}, x = 18 0^{\circ} - 0.33983 \dots + 36 0^{\circ} n - 1 0^{\circ}

Solution steps

csc (x + 1 0^{\circ}) = 3

Apply trig inverse properties

x + 1 0^{\circ} = arccsc (3) + 36 0^{\circ} n, x + 1 0^{\circ} = 18 0^{\circ} - arccsc (3) + 36 0^{\circ} n

Solve

x + 1 0^{\circ} = arccsc (3) + 36 0^{\circ} n : x = arccsc (3) + 36 0^{\circ} n - 1 0^{\circ}

Solve

x + 1 0^{\circ} = 18 0^{\circ} - arccsc (3) + 36 0^{\circ} n : x = 18 0^{\circ} - arccsc (3) + 36 0^{\circ} n - 1 0^{\circ}

x = arccsc (3) + 36 0^{\circ} n - 1 0^{\circ}, x = 18 0^{\circ} - arccsc (3) + 36 0^{\circ} n - 1 0^{\circ}

Show solutions in decimal form

x = 0.33983 \dots + 36 0^{\circ} n - 1 0^{\circ}, x = 18 0^{\circ} - 0.33983 \dots + 36 0^{\circ} n - 1 0^{\circ}

6 tan (x) = 18 cot (x)

9 cos (x) = 0

18 arcsin (x) = 3 π

(2 cos (x) - 3) (2 sin (x) - 1) = 0

11 tan (θ) - 10 = 4 tan (θ) - 4

What is the general solution for csc(x+10)=3 ?
The general solution for csc(x+10)=3 is x=0.33983…+360n-10,x=180-0.33983…+360n-10