What is the general solution for cos(x+40)=0.85 ?

The general solution for cos(x+40)=0.85 is x=0.55481…+360n-40,x=360-0.55481…+360n-40

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cos(x+40)=0.85

cos (x + 4 0^{\circ}) = 0.85

x = 0.55481 \dots + 36 0^{\circ} n - 4 0^{\circ}, x = 36 0^{\circ} - 0.55481 \dots + 36 0^{\circ} n - 4 0^{\circ}

Solution steps

cos (x + 4 0^{\circ}) = 0.85

Apply trig inverse properties

x + 4 0^{\circ} = arccos (0.85) + 36 0^{\circ} n, x + 4 0^{\circ} = 36 0^{\circ} - arccos (0.85) + 36 0^{\circ} n

Solve

x + 4 0^{\circ} = arccos (0.85) + 36 0^{\circ} n : x = arccos (0.85) + 36 0^{\circ} n - 4 0^{\circ}

Solve

x + 4 0^{\circ} = 36 0^{\circ} - arccos (0.85) + 36 0^{\circ} n : x = 36 0^{\circ} - arccos (0.85) + 36 0^{\circ} n - 4 0^{\circ}

x = arccos (0.85) + 36 0^{\circ} n - 4 0^{\circ}, x = 36 0^{\circ} - arccos (0.85) + 36 0^{\circ} n - 4 0^{\circ}

Show solutions in decimal form

x = 0.55481 \dots + 36 0^{\circ} n - 4 0^{\circ}, x = 36 0^{\circ} - 0.55481 \dots + 36 0^{\circ} n - 4 0^{\circ}

sin^{2} (a) = 1 - cos (2 a)

cos^{4} (x) = cos^{2} (x)

tan (x) = 2 + tan^{3} (x)

2 \cdot sin (a) = sin (3 a)

\frac{cos ( x ) + 5 sin ( x )}{2 - 3} = 0

What is the general solution for cos(x+40)=0.85 ?
The general solution for cos(x+40)=0.85 is x=0.55481…+360n-40,x=360-0.55481…+360n-40