What is the general solution for sin(x)=cos(40) ?

The general solution for sin(x)=cos(40) is x=360n+50,x=180-50+360n

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sin(x)=cos(40)

sin (x) = cos (4 0^{\circ})

x = 36 0^{\circ} n + 5 0^{\circ}, x = 18 0^{\circ} - 5 0^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = cos (4 0^{\circ})

Rewrite using trig identities

sin (x) = sin (9 0^{\circ} - 4 0^{\circ})

Apply trig inverse properties

x = 9 0^{\circ} - 4 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} - (9 0^{\circ} - 4 0^{\circ}) + 36 0^{\circ} n

x = 9 0^{\circ} - 4 0^{\circ} + 36 0^{\circ} n : x = 36 0^{\circ} n + 5 0^{\circ}

x = 18 0^{\circ} - (9 0^{\circ} - 4 0^{\circ}) + 36 0^{\circ} n : x = 18 0^{\circ} - 5 0^{\circ} + 36 0^{\circ} n

x = 36 0^{\circ} n + 5 0^{\circ}, x = 18 0^{\circ} - 5 0^{\circ} + 36 0^{\circ} n

tan (x) = \frac{2.5}{2}

sin (2 x) cos (x) + sin (x) cos (2 x) = - \frac{1}{2}

5 cos (x) + 2 = 3 cos (x), 0 \leq x \leq 2 π

2 tan (2 x + 10) = - 5.5

sin (t) = sin (2 t)

What is the general solution for sin(x)=cos(40) ?
The general solution for sin(x)=cos(40) is x=360n+50,x=180-50+360n