What is the general solution for sin(47)=cos(x) ?

The general solution for sin(47)=cos(x) is x=0.75049…+360n,x=360-0.75049…+360n

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sin(47)=cos(x)

sin (4 7^{\circ}) = cos (x)

x = 0.75049 \dots + 36 0^{\circ} n, x = 36 0^{\circ} - 0.75049 \dots + 36 0^{\circ} n

Radians

x = 0.75049 \dots + 2 πn, x = 2 π - 0.75049 \dots + 2 πn

Solution steps

sin (4 7^{\circ}) = cos (x)

Switch sides

cos (x) = sin (4 7^{\circ})

Apply trig inverse properties

cos (x) = sin (4 7^{\circ})

General solutions for

cos (x) = sin (4 7^{\circ})

cos (x) = a \Rightarrow x = arccos (a) + 36 0^{\circ} n, x = 36 0^{\circ} - arccos (a) + 36 0^{\circ} n

x = arccos (sin (4 7^{\circ})) + 36 0^{\circ} n, x = 36 0^{\circ} - arccos (sin (4 7^{\circ})) + 36 0^{\circ} n

x = arccos (sin (4 7^{\circ})) + 36 0^{\circ} n, x = 36 0^{\circ} - arccos (sin (4 7^{\circ})) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.75049 \dots + 36 0^{\circ} n, x = 36 0^{\circ} - 0.75049 \dots + 36 0^{\circ} n

0.82 = 0.102 cos (3.715 t)

sin^{2} (x) + 0.49 = 1

6 cos^{2} (θ) + sin^{2} (θ) = 4

15 sin (3 0^{\circ}) = 10 sin (x)

sin (0) = - sin (o) cos (0)

What is the general solution for sin(47)=cos(x) ?
The general solution for sin(47)=cos(x) is x=0.75049…+360n,x=360-0.75049…+360n