What is the general solution for cos(θ)=0.7071 ?

The general solution for cos(θ)=0.7071 is θ=0.78540…+2pin,θ=2pi-0.78540…+2pin

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cos(θ)=0.7071

cos (θ) = 0.7071

θ = 0.78540 \dots + 2 πn, θ = 2 π - 0.78540 \dots + 2 πn

Degrees

θ = 45.00054 \dots^{\circ} + 36 0^{\circ} n, θ = 314.99945 \dots^{\circ} + 36 0^{\circ} n

Solution steps

cos (θ) = 0.7071

Apply trig inverse properties

cos (θ) = 0.7071

General solutions for

cos (θ) = 0.7071

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

θ = arccos (0.7071) + 2 πn, θ = 2 π - arccos (0.7071) + 2 πn

θ = arccos (0.7071) + 2 πn, θ = 2 π - arccos (0.7071) + 2 πn

Show solutions in decimal form

θ = 0.78540 \dots + 2 πn, θ = 2 π - 0.78540 \dots + 2 πn

2 cos (x) - 5 sin (x) = 0

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

sin (3 0^{\circ}) = cos (2 x)

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

3 sec (x) - cos (x) - 2 = 0

What is the general solution for cos(θ)=0.7071 ?
The general solution for cos(θ)=0.7071 is θ=0.78540…+2pin,θ=2pi-0.78540…+2pin