What is the general solution for 2/5 =cos(θ) ?

The general solution for 2/5 =cos(θ) is θ=1.15927…+2pin,θ=2pi-1.15927…+2pin

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2/5 =cos(θ)

\frac{2}{5} = cos (θ)

θ = 1.15927 \dots + 2 πn, θ = 2 π - 1.15927 \dots + 2 πn

Degrees

θ = 66.42182 \dots^{\circ} + 36 0^{\circ} n, θ = 293.57817 \dots^{\circ} + 36 0^{\circ} n

Solution steps

\frac{2}{5} = cos (θ)

Switch sides

cos (θ) = \frac{2}{5}

Apply trig inverse properties

cos (θ) = \frac{2}{5}

General solutions for

cos (θ) = \frac{2}{5}

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

θ = arccos (\frac{2}{5}) + 2 πn, θ = 2 π - arccos (\frac{2}{5}) + 2 πn

θ = arccos (\frac{2}{5}) + 2 πn, θ = 2 π - arccos (\frac{2}{5}) + 2 πn

Show solutions in decimal form

θ = 1.15927 \dots + 2 πn, θ = 2 π - 1.15927 \dots + 2 πn

2 - 2 cos^{2} (x) = sin (x)

cos (x) = \frac{6}{7}

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

csc^{2} (x) = 2 csc (x)

cos (x) - 3 sin (x) = 0

What is the general solution for 2/5 =cos(θ) ?
The general solution for 2/5 =cos(θ) is θ=1.15927…+2pin,θ=2pi-1.15927…+2pin