What is the general solution for cos(20)=sin(x) ?

The general solution for cos(20)=sin(x) is x=360n+70,x=180-70+360n

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cos(20)=sin(x)

cos (2 0^{\circ}) = sin (x)

x = 36 0^{\circ} n + 7 0^{\circ}, x = 18 0^{\circ} - 7 0^{\circ} + 36 0^{\circ} n

Solution steps

cos (2 0^{\circ}) = sin (x)

Switch sides

sin (x) = cos (2 0^{\circ})

Rewrite using trig identities

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

Apply trig inverse properties

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

x = 9 0^{\circ} - 2 0^{\circ} + 36 0^{\circ} n : x = 36 0^{\circ} n + 7 0^{\circ}

x = 18 0^{\circ} - (9 0^{\circ} - 2 0^{\circ}) + 36 0^{\circ} n : x = 18 0^{\circ} - 7 0^{\circ} + 36 0^{\circ} n

x = 36 0^{\circ} n + 7 0^{\circ}, x = 18 0^{\circ} - 7 0^{\circ} + 36 0^{\circ} n

2 cos (x) + sec (x) = 0

sec (2 x) = 1

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

2 cos^{2} (x) + sin^{2} (x) = 0

9.383 = 3.1915 cos (\frac{π}{6 ( 1 - c )}) + 6.1915

What is the general solution for cos(20)=sin(x) ?
The general solution for cos(20)=sin(x) is x=360n+70,x=180-70+360n