What is the general solution for cos(2a)= 31/81 ?

The general solution for cos(2a)= 31/81 is a=(1.17806…)/2+pin,a=pi-(1.17806…)/2+pin

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cos(2a)= 31/81

cos (2 a) = \frac{31}{81}

a = \frac{1.17806 \dots}{2} + πn, a = π - \frac{1.17806 \dots}{2} + πn

Degrees

a = 33.74898 \dots^{\circ} + 18 0^{\circ} n, a = 146.25101 \dots^{\circ} + 18 0^{\circ} n

Solution steps

cos (2 a) = \frac{31}{81}

Apply trig inverse properties

cos (2 a) = \frac{31}{81}

General solutions for

cos (2 a) = \frac{31}{81}

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

2 a = arccos (\frac{31}{81}) + 2 πn, 2 a = 2 π - arccos (\frac{31}{81}) + 2 πn

2 a = arccos (\frac{31}{81}) + 2 πn, 2 a = 2 π - arccos (\frac{31}{81}) + 2 πn

Solve

2 a = arccos (\frac{31}{81}) + 2 πn : a = \frac{arccos ( \frac{31}{81} )}{2} + πn

2 a = arccos (\frac{31}{81}) + 2 πn

Divide both sides by

2

2 a = arccos (\frac{31}{81}) + 2 πn

Divide both sides by

2

\frac{2 a}{2} = \frac{arccos ( \frac{31}{81} )}{2} + \frac{2 πn}{2}

Simplify

a = \frac{arccos ( \frac{31}{81} )}{2} + πn

a = \frac{arccos ( \frac{31}{81} )}{2} + πn

Solve

2 a = 2 π - arccos (\frac{31}{81}) + 2 πn : a = π - \frac{arccos ( \frac{31}{81} )}{2} + πn

2 a = 2 π - arccos (\frac{31}{81}) + 2 πn

Divide both sides by

2

2 a = 2 π - arccos (\frac{31}{81}) + 2 πn

Divide both sides by

2

\frac{2 a}{2} = \frac{2 π}{2} - \frac{arccos ( \frac{31}{81} )}{2} + \frac{2 πn}{2}

Simplify

a = π - \frac{arccos ( \frac{31}{81} )}{2} + πn

a = π - \frac{arccos ( \frac{31}{81} )}{2} + πn

a = \frac{arccos ( \frac{31}{81} )}{2} + πn, a = π - \frac{arccos ( \frac{31}{81} )}{2} + πn

Show solutions in decimal form

a = \frac{1.17806 \dots}{2} + πn, a = π - \frac{1.17806 \dots}{2} + πn

\frac{tan ( a ) + 1}{tan ( a )} = 2

1 - cos (x) = \frac{2 sin ^{2} ( x )}{2}

2 sec (2 x) + tan (2 x) - 3 = 0

x, 5 = 9.4 cos (x)

20 = 2.891 sin (0.016 d - 1.183) + 18.512

What is the general solution for cos(2a)= 31/81 ?
The general solution for cos(2a)= 31/81 is a=(1.17806…)/2+pin,a=pi-(1.17806…)/2+pin