What is the general solution for sqrt(8)cos(θ)+7=-6cos(θ)+sqrt(5) ?

The general solution for sqrt(8)cos(θ)+7=-6cos(θ)+sqrt(5) is θ=2.14077…+2pin,θ=-2.14077…+2pin

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sqrt(8)cos(θ)+7=-6cos(θ)+sqrt(5)

8 cos (θ) + 7 = - 6 cos (θ) + 5

θ = 2.14077 \dots + 2 πn, θ = - 2.14077 \dots + 2 πn

Solution steps

8 cos (θ) + 7 = - 6 cos (θ) + 5

Solve by substitution

cos (θ) = \frac{( 5 - 7 ) ( 3 - 2 )}{14}

cos (θ) = \frac{( 5 - 7 ) ( 3 - 2 )}{14} : θ = arccos (\frac{( 5 - 7 ) ( 3 - 2 )}{14}) + 2 πn, θ = - arccos (\frac{( 5 - 7 ) ( 3 - 2 )}{14}) + 2 πn

Combine all the solutions

θ = arccos (\frac{( 5 - 7 ) ( 3 - 2 )}{14}) + 2 πn, θ = - arccos (\frac{( 5 - 7 ) ( 3 - 2 )}{14}) + 2 πn

Show solutions in decimal form

θ = 2.14077 \dots + 2 πn, θ = - 2.14077 \dots + 2 πn

8 sin (θ) + 15 cos (θ) = 17

8 sin (θ) + 15 cos (θ) = 14

cos (x - 1) = 0

2 sin (t) + 3 cos (t) = 0

tan (θ) = \frac{- \frac{11}{3} - ( - \frac{4}{3} )}{1 + ( - \frac{4}{3} ) ( - \frac{11}{3} )}

What is the general solution for sqrt(8)cos(θ)+7=-6cos(θ)+sqrt(5) ?
The general solution for sqrt(8)cos(θ)+7=-6cos(θ)+sqrt(5) is θ=2.14077…+2pin,θ=-2.14077…+2pin