What is the general solution for 1/4 =cos(x) ?

The general solution for 1/4 =cos(x) is x=1.31811…+2pin,x=2pi-1.31811…+2pin

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1/4 =cos(x)

\frac{1}{4} = cos (x)

x = 1.31811 \dots + 2 πn, x = 2 π - 1.31811 \dots + 2 πn

Degrees

x = 75.52248 \dots^{\circ} + 36 0^{\circ} n, x = 284.47751 \dots^{\circ} + 36 0^{\circ} n

Solution steps

\frac{1}{4} = cos (x)

Switch sides

cos (x) = \frac{1}{4}

Apply trig inverse properties

cos (x) = \frac{1}{4}

General solutions for

cos (x) = \frac{1}{4}

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

x = arccos (\frac{1}{4}) + 2 πn, x = 2 π - arccos (\frac{1}{4}) + 2 πn

x = arccos (\frac{1}{4}) + 2 πn, x = 2 π - arccos (\frac{1}{4}) + 2 πn

Show solutions in decimal form

x = 1.31811 \dots + 2 πn, x = 2 π - 1.31811 \dots + 2 πn

cos (2 x) + 3 cos (x) = - 2

4 tan^{2} (θ) + 16 tan (θ) = 7 tan (θ) - 2

10 (1 - cos (θ)) = sin^{2} (θ)

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

tan (x - 20) = cot (x + 45)

What is the general solution for 1/4 =cos(x) ?
The general solution for 1/4 =cos(x) is x=1.31811…+2pin,x=2pi-1.31811…+2pin