What is the general solution for csc(2x+3)= 5/4 ?

The general solution for csc(2x+3)= 5/4 is x=180n-1.5+(0.92729…)/2 ,x=180n+90-1.5-(0.92729…)/2

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csc(2x+3)= 5/4

csc (2 x + 3^{\circ}) = \frac{5}{4}

x = 18 0^{\circ} n - 1. 5^{\circ} + \frac{0.92729 \dots}{2}, x = 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{0.92729 \dots}{2}

Solution steps

csc (2 x + 3^{\circ}) = \frac{5}{4}

Apply trig inverse properties

2 x + 3^{\circ} = arccsc (\frac{5}{4}) + 36 0^{\circ} n, 2 x + 3^{\circ} = 18 0^{\circ} - arccsc (\frac{5}{4}) + 36 0^{\circ} n

Solve

2 x + 3^{\circ} = arccsc (\frac{5}{4}) + 36 0^{\circ} n : x = 18 0^{\circ} n - 1. 5^{\circ} + \frac{arccsc ( \frac{5}{4} )}{2}

Solve

2 x + 3^{\circ} = 18 0^{\circ} - arccsc (\frac{5}{4}) + 36 0^{\circ} n : x = 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2}

x = 18 0^{\circ} n - 1. 5^{\circ} + \frac{arccsc ( \frac{5}{4} )}{2}, x = 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2}

Show solutions in decimal form

x = 18 0^{\circ} n - 1. 5^{\circ} + \frac{0.92729 \dots}{2}, x = 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{0.92729 \dots}{2}

4 cos^{2} (θ) - cos (θ) - 9 = 7 cos (θ) - 4

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

cos (x) = 0.998482

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

(- 6 cos (x) - 5 sin (x))^{2} + 11 sin^{2} (x) = 51

What is the general solution for csc(2x+3)= 5/4 ?
The general solution for csc(2x+3)= 5/4 is x=180n-1.5+(0.92729…)/2 ,x=180n+90-1.5-(0.92729…)/2