What is the general solution for cos(θ)=0.8126 ?

The general solution for cos(θ)=0.8126 is θ=0.62219…+2pin,θ=2pi-0.62219…+2pin

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cos(θ)=0.8126

cos (θ) = 0.8126

θ = 0.62219 \dots + 2 πn, θ = 2 π - 0.62219 \dots + 2 πn

Degrees

θ = 35.64925 \dots^{\circ} + 36 0^{\circ} n, θ = 324.35074 \dots^{\circ} + 36 0^{\circ} n

Solution steps

cos (θ) = 0.8126

Apply trig inverse properties

cos (θ) = 0.8126

General solutions for

cos (θ) = 0.8126

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

θ = arccos (0.8126) + 2 πn, θ = 2 π - arccos (0.8126) + 2 πn

θ = arccos (0.8126) + 2 πn, θ = 2 π - arccos (0.8126) + 2 πn

Show solutions in decimal form

θ = 0.62219 \dots + 2 πn, θ = 2 π - 0.62219 \dots + 2 πn

0 = 2 + cos (θ)

8 tan (\frac{x}{2}) + 8 cos (x) tan (\frac{x}{2}) = 1, 0^{\circ} < x < 36 0^{\circ}

cos (θ) = - \frac{4}{5}, tan (θ) < 0

16 sin^{2} (x) = 8

- 2 cot (x) = 0

What is the general solution for cos(θ)=0.8126 ?
The general solution for cos(θ)=0.8126 is θ=0.62219…+2pin,θ=2pi-0.62219…+2pin