What is the general solution for cos(2θ)=0.4 ?

The general solution for cos(2θ)=0.4 is θ=(1.15927…)/2+pin,θ=pi-(1.15927…)/2+pin

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cos(2θ)=0.4

cos (2 θ) = 0.4

θ = \frac{1.15927 \dots}{2} + πn, θ = π - \frac{1.15927 \dots}{2} + πn

Solution steps

cos (2 θ) = 0.4

Apply trig inverse properties

2 θ = arccos (0.4) + 2 πn, 2 θ = 2 π - arccos (0.4) + 2 πn

Solve

2 θ = arccos (0.4) + 2 πn : θ = \frac{arccos ( 0.4 )}{2} + πn

Solve

2 θ = 2 π - arccos (0.4) + 2 πn : θ = π - \frac{arccos ( 0.4 )}{2} + πn

θ = \frac{arccos ( 0.4 )}{2} + πn, θ = π - \frac{arccos ( 0.4 )}{2} + πn

Show solutions in decimal form

θ = \frac{1.15927 \dots}{2} + πn, θ = π - \frac{1.15927 \dots}{2} + πn

6 sin (x) + 2 cos (x) = 0

cos (2 x) = - \frac{3}{2}, 0 \leq x \leq 2 π

tan (θ) = \frac{5}{2}

sin^{2} (θ) = 7 (cos (- θ) + 1)

4 csc (2 θ) + 8 = 0

What is the general solution for cos(2θ)=0.4 ?
The general solution for cos(2θ)=0.4 is θ=(1.15927…)/2+pin,θ=pi-(1.15927…)/2+pin