What is the general solution for 209cos(47)=150cos(θ) ?

The general solution for 209cos(47)=150cos(θ) is θ=0.31675…+360n,θ=360-0.31675…+360n

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209cos(47)=150cos(θ)

209 cos (4 7^{\circ}) = 150 cos (θ)

θ = 0.31675 \dots + 36 0^{\circ} n, θ = 36 0^{\circ} - 0.31675 \dots + 36 0^{\circ} n

Radians

θ = 0.31675 \dots + 2 πn, θ = 2 π - 0.31675 \dots + 2 πn

Solution steps

209 cos (4 7^{\circ}) = 150 cos (θ)

Switch sides

150 cos (θ) = 209 cos (4 7^{\circ})

Divide both sides by

150

150 cos (θ) = 209 cos (4 7^{\circ})

Divide both sides by

150

\frac{150 cos ( θ )}{150} = \frac{209 cos ( 4 7 ^{\circ} )}{150}

Simplify

cos (θ) = \frac{209 cos ( 4 7 ^{\circ} )}{150}

cos (θ) = \frac{209 cos ( 4 7 ^{\circ} )}{150}

Apply trig inverse properties

cos (θ) = \frac{209 cos ( 4 7 ^{\circ} )}{150}

General solutions for

cos (θ) = \frac{209 cos ( 4 7 ^{\circ} )}{150}

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

θ = arccos (\frac{209 cos ( 4 7 ^{\circ} )}{150}) + 36 0^{\circ} n, θ = 36 0^{\circ} - arccos (\frac{209 cos ( 4 7 ^{\circ} )}{150}) + 36 0^{\circ} n

θ = arccos (\frac{209 cos ( 4 7 ^{\circ} )}{150}) + 36 0^{\circ} n, θ = 36 0^{\circ} - arccos (\frac{209 cos ( 4 7 ^{\circ} )}{150}) + 36 0^{\circ} n

Show solutions in decimal form

θ = 0.31675 \dots + 36 0^{\circ} n, θ = 36 0^{\circ} - 0.31675 \dots + 36 0^{\circ} n

7 - 5 cos (x) = 10, 7 - 5 cos (x) = 10

cos (4 x) = cos (x)

- 4 cos (2 θ) - 19 = - 26 cos (θ), 0 \leq θ < 36 0^{\circ}

3 cos^{2} (x) = 7 - 8 sin (x)

sin (X) = - \frac{1}{2}

What is the general solution for 209cos(47)=150cos(θ) ?
The general solution for 209cos(47)=150cos(θ) is θ=0.31675…+360n,θ=360-0.31675…+360n