What is the general solution for cos(θ)= 7/8 ?

The general solution for cos(θ)= 7/8 is θ=0.50536…+2pin,θ=2pi-0.50536…+2pin

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cos(θ)= 7/8

cos (θ) = \frac{7}{8}

θ = 0.50536 \dots + 2 πn, θ = 2 π - 0.50536 \dots + 2 πn

Solution steps

cos (θ) = \frac{7}{8}

Apply trig inverse properties

θ = arccos (\frac{7}{8}) + 2 πn, θ = 2 π - arccos (\frac{7}{8}) + 2 πn

Show solutions in decimal form

θ = 0.50536 \dots + 2 πn, θ = 2 π - 0.50536 \dots + 2 πn

sec (x) (2 sin (x) + 1) - 2 (2 sin (x) + 1) = 0

3 sin^{2} (x) + 2 cos (2 x) = 1

1 = sin (x) + 3 cos (x)

1 + sin (x) = 2 cos^{2} (x), 0 \leq x < 5

2 - 3 cos (x) = 5 + 3 cos (x)

What is the general solution for cos(θ)= 7/8 ?
The general solution for cos(θ)= 7/8 is θ=0.50536…+2pin,θ=2pi-0.50536…+2pin