What is the general solution for cos(θ)=(25)/(sqrt(714)) ?

The general solution for cos(θ)=(25)/(sqrt(714)) is θ=0.36083…+2pin,θ=2pi-0.36083…+2pin

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cos(θ)=(25)/(sqrt(714))

cos (θ) = \frac{25}{714}

θ = 0.36083 \dots + 2 πn, θ = 2 π - 0.36083 \dots + 2 πn

Radians

θ = 0.36083 \dots + 6.28318 \dots n, θ = 5.92234 \dots + 6.28318 \dots n

Solution steps

cos (θ) = \frac{25}{714}

Simplify

\frac{25}{714} : \frac{25 714}{714}

\frac{25}{714}

Multiply by the conjugate

\frac{714}{714}

= \frac{25 714}{714 714}

714714 = 714

714714

Apply radical rule:

a a = a

714714 = 714

= 714

= \frac{25 714}{714}

cos (θ) = \frac{25 714}{714}

Apply trig inverse properties

cos (θ) = \frac{25 714}{714}

General solutions for

cos (θ) = \frac{25 714}{714}

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

θ = arccos (\frac{25 714}{714}) + 2 πn, θ = 2 π - arccos (\frac{25 714}{714}) + 2 πn

θ = arccos (\frac{25 714}{714}) + 2 πn, θ = 2 π - arccos (\frac{25 714}{714}) + 2 πn

Show solutions in decimal form

θ = 0.36083 \dots + 2 πn, θ = 2 π - 0.36083 \dots + 2 πn

3 sec^{2} (x) - 4 = 0, 0 \leq x < 2 π

3 cos (2 x) + 7 sin (x) - 5 = 0

cos^{2} (θ) = \frac{1}{3}

x, sin (\frac{x}{5}) = - \frac{3}{2}

sin (B) = \frac{3}{10}

What is the general solution for cos(θ)=(25)/(sqrt(714)) ?
The general solution for cos(θ)=(25)/(sqrt(714)) is θ=0.36083…+2pin,θ=2pi-0.36083…+2pin