What is the general solution for sin(x)=cos(2x+51) ?

The general solution for sin(x)=cos(2x+51) is x=(21600n+2340)/(180),x=-(8460+21600n)/(60)

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sin(x)=cos(2x+51)

sin (x) = cos (2 x + 5 1^{\circ})

x = \frac{2160 0 ^{\circ} n + 234 0 ^{\circ}}{180}, x = - \frac{846 0 ^{\circ} + 2160 0 ^{\circ} n}{60}

Solution steps

sin (x) = cos (2 x + 5 1^{\circ})

Rewrite using trig identities

sin (x) = sin (9 0^{\circ} - (2 x + 5 1^{\circ}))

Apply trig inverse properties

x = 9 0^{\circ} - (2 x + 5 1^{\circ}) + 36 0^{\circ} n, x = 18 0^{\circ} - (9 0^{\circ} - (2 x + 5 1^{\circ})) + 36 0^{\circ} n

x = 9 0^{\circ} - (2 x + 5 1^{\circ}) + 36 0^{\circ} n : x = \frac{2160 0 ^{\circ} n + 234 0 ^{\circ}}{180}

x = 18 0^{\circ} - (9 0^{\circ} - (2 x + 5 1^{\circ})) + 36 0^{\circ} n : x = - \frac{846 0 ^{\circ} + 2160 0 ^{\circ} n}{60}

x = \frac{2160 0 ^{\circ} n + 234 0 ^{\circ}}{180}, x = - \frac{846 0 ^{\circ} + 2160 0 ^{\circ} n}{60}

sin (x) = \frac{π}{4}

cos (x) = 45.7

- 2 cos (2 θ) = 1

tan (5 x) \cdot cot (x + 4 0^{\circ}) = 1

sin (θ) = 0.7043

What is the general solution for sin(x)=cos(2x+51) ?
The general solution for sin(x)=cos(2x+51) is x=(21600n+2340)/(180),x=-(8460+21600n)/(60)