What is the general solution for cos(x-30)=0.22 ?

The general solution for cos(x-30)=0.22 is x=1.34898…+360n+30,x=360-1.34898…+360n+30

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cos(x-30)=0.22

cos (x - 3 0^{\circ}) = 0.22

x = 1.34898 \dots + 36 0^{\circ} n + 3 0^{\circ}, x = 36 0^{\circ} - 1.34898 \dots + 36 0^{\circ} n + 3 0^{\circ}

Radians

x = 1.34898 \dots + \frac{π}{6} + 2 πn, x = 2 π - 1.34898 \dots + \frac{π}{6} + 2 πn

Solution steps

cos (x - 3 0^{\circ}) = 0.22

Apply trig inverse properties

cos (x - 3 0^{\circ}) = 0.22

General solutions for

cos (x - 3 0^{\circ}) = 0.22

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

x - 3 0^{\circ} = arccos (0.22) + 36 0^{\circ} n, x - 3 0^{\circ} = 36 0^{\circ} - arccos (0.22) + 36 0^{\circ} n

x - 3 0^{\circ} = arccos (0.22) + 36 0^{\circ} n, x - 3 0^{\circ} = 36 0^{\circ} - arccos (0.22) + 36 0^{\circ} n

Solve

x - 3 0^{\circ} = arccos (0.22) + 36 0^{\circ} n : x = arccos (0.22) + 36 0^{\circ} n + 3 0^{\circ}

x - 3 0^{\circ} = arccos (0.22) + 36 0^{\circ} n

Move

3 0^{\circ}

to the right side

x - 3 0^{\circ} = arccos (0.22) + 36 0^{\circ} n

Add

3 0^{\circ}

to both sides

x - 3 0^{\circ} + 3 0^{\circ} = arccos (0.22) + 36 0^{\circ} n + 3 0^{\circ}

Simplify

x = arccos (0.22) + 36 0^{\circ} n + 3 0^{\circ}

x = arccos (0.22) + 36 0^{\circ} n + 3 0^{\circ}

Solve

x - 3 0^{\circ} = 36 0^{\circ} - arccos (0.22) + 36 0^{\circ} n : x = 36 0^{\circ} - arccos (0.22) + 36 0^{\circ} n + 3 0^{\circ}

x - 3 0^{\circ} = 36 0^{\circ} - arccos (0.22) + 36 0^{\circ} n

Move

3 0^{\circ}

to the right side

x - 3 0^{\circ} = 36 0^{\circ} - arccos (0.22) + 36 0^{\circ} n

Add

3 0^{\circ}

to both sides

x - 3 0^{\circ} + 3 0^{\circ} = 36 0^{\circ} - arccos (0.22) + 36 0^{\circ} n + 3 0^{\circ}

Simplify

x = 36 0^{\circ} - arccos (0.22) + 36 0^{\circ} n + 3 0^{\circ}

x = 36 0^{\circ} - arccos (0.22) + 36 0^{\circ} n + 3 0^{\circ}

x = arccos (0.22) + 36 0^{\circ} n + 3 0^{\circ}, x = 36 0^{\circ} - arccos (0.22) + 36 0^{\circ} n + 3 0^{\circ}

Show solutions in decimal form

x = 1.34898 \dots + 36 0^{\circ} n + 3 0^{\circ}, x = 36 0^{\circ} - 1.34898 \dots + 36 0^{\circ} n + 3 0^{\circ}

sin (4 x - 22) = cos (6 x - 13)

cos (2 x) + 1 = 2

csc (x) = - \frac{3}{5}

cos (x) = \frac{3}{5}, cos (2 π + x)

sin (4 5^{\circ}) = 1.57 \cdot sin (θ)

What is the general solution for cos(x-30)=0.22 ?
The general solution for cos(x-30)=0.22 is x=1.34898…+360n+30,x=360-1.34898…+360n+30