What is the general solution for 885cos(θ)-70=cos(250) ?

The general solution for 885cos(θ)-70=cos(250) is θ=1.49200…+360n,θ=360-1.49200…+360n

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885cos(θ)-70=cos(250)

885 cos (θ) - 70 = cos (25 0^{\circ})

θ = 1.49200 \dots + 36 0^{\circ} n, θ = 36 0^{\circ} - 1.49200 \dots + 36 0^{\circ} n

Radians

θ = 1.49200 \dots + 2 πn, θ = 2 π - 1.49200 \dots + 2 πn

Solution steps

885 cos (θ) - 70 = cos (25 0^{\circ})

Move

70

to the right side

885 cos (θ) - 70 = cos (25 0^{\circ})

Add

70

to both sides

885 cos (θ) - 70 + 70 = cos (25 0^{\circ}) + 70

Simplify

885 cos (θ) = cos (25 0^{\circ}) + 70

885 cos (θ) = cos (25 0^{\circ}) + 70

Divide both sides by

885

885 cos (θ) = cos (25 0^{\circ}) + 70

Divide both sides by

885

\frac{885 cos ( θ )}{885} = \frac{cos ( 25 0 ^{\circ} )}{885} + \frac{70}{885}

Simplify

\frac{885 cos ( θ )}{885} = \frac{cos ( 25 0 ^{\circ} )}{885} + \frac{70}{885}

Simplify

\frac{885 cos ( θ )}{885} : cos (θ)

\frac{885 cos ( θ )}{885}

Divide the numbers:

\frac{885}{885} = 1

= cos (θ)

Simplify

\frac{cos ( 25 0 ^{\circ} )}{885} + \frac{70}{885} : \frac{cos ( 25 0 ^{\circ} ) + 70}{885}

\frac{cos ( 25 0 ^{\circ} )}{885} + \frac{70}{885}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{cos ( 25 0 ^{\circ} ) + 70}{885}

cos (θ) = \frac{cos ( 25 0 ^{\circ} ) + 70}{885}

cos (θ) = \frac{cos ( 25 0 ^{\circ} ) + 70}{885}

cos (θ) = \frac{cos ( 25 0 ^{\circ} ) + 70}{885}

Apply trig inverse properties

cos (θ) = \frac{cos ( 25 0 ^{\circ} ) + 70}{885}

General solutions for

cos (θ) = \frac{cos ( 25 0 ^{\circ} ) + 70}{885}

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

θ = arccos (\frac{cos ( 25 0 ^{\circ} ) + 70}{885}) + 36 0^{\circ} n, θ = 36 0^{\circ} - arccos (\frac{cos ( 25 0 ^{\circ} ) + 70}{885}) + 36 0^{\circ} n

θ = arccos (\frac{cos ( 25 0 ^{\circ} ) + 70}{885}) + 36 0^{\circ} n, θ = 36 0^{\circ} - arccos (\frac{cos ( 25 0 ^{\circ} ) + 70}{885}) + 36 0^{\circ} n

Show solutions in decimal form

θ = 1.49200 \dots + 36 0^{\circ} n, θ = 36 0^{\circ} - 1.49200 \dots + 36 0^{\circ} n

What is the general solution for 885cos(θ)-70=cos(250) ?
The general solution for 885cos(θ)-70=cos(250) is θ=1.49200…+360n,θ=360-1.49200…+360n