What is the general solution for cos(c)=cos(7)cos(60) ?

The general solution for cos(c)=cos(7)cos(60) is c=1.18429…+360n,c=360-1.18429…+360n

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cos(c)=cos(7)cos(60)

cos (c) = cos (7) cos (6 0^{\circ})

c = 1.18429 \dots + 36 0^{\circ} n, c = 36 0^{\circ} - 1.18429 \dots + 36 0^{\circ} n

Radians

c = 1.18429 \dots + 2 πn, c = 2 π - 1.18429 \dots + 2 πn

Solution steps

cos (c) = cos (7) cos (6 0^{\circ})

cos (6 0^{\circ}) = \frac{1}{2}

cos (6 0^{\circ})

Use the following trivial identity:

cos (6 0^{\circ}) = \frac{1}{2}

cos (6 0^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{1}{2}

= \frac{1}{2}

cos (c) = cos (7) \frac{1}{2}

Apply trig inverse properties

cos (c) = cos (7) \frac{1}{2}

General solutions for

cos (c) = cos (7) \frac{1}{2}

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

c = arccos (cos (7) \frac{1}{2}) + 36 0^{\circ} n, c = 36 0^{\circ} - arccos (cos (7) \frac{1}{2}) + 36 0^{\circ} n

c = arccos (cos (7) \frac{1}{2}) + 36 0^{\circ} n, c = 36 0^{\circ} - arccos (cos (7) \frac{1}{2}) + 36 0^{\circ} n

Show solutions in decimal form

c = 1.18429 \dots + 36 0^{\circ} n, c = 36 0^{\circ} - 1.18429 \dots + 36 0^{\circ} n

cos (x π) = (- 1)^{n}

3 csc (θ) = 4.5

cos^{3} (x) = \frac{1}{4 ( 3 cos ( x ) + cos ( 3 x ) )}

w, s (t) = A e^{- c t} cos (wt + θ)

2 = 2 sin (x)

What is the general solution for cos(c)=cos(7)cos(60) ?
The general solution for cos(c)=cos(7)cos(60) is c=1.18429…+360n,c=360-1.18429…+360n