What is the general solution for 3cos(5x)=2 ?

The general solution for 3cos(5x)=2 is x=(0.84106…)/5+(2pin)/5 ,x=(2pi)/5-(0.84106…)/5+(2pin)/5

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3cos(5x)=2

3 cos (5 x) = 2

x = \frac{0.84106 \dots}{5} + \frac{2 πn}{5}, x = \frac{2 π}{5} - \frac{0.84106 \dots}{5} + \frac{2 πn}{5}

Degrees

x = 9.63793 \dots^{\circ} + 7 2^{\circ} n, x = 62.36206 \dots^{\circ} + 7 2^{\circ} n

Solution steps

3 cos (5 x) = 2

Divide both sides by

3

3 cos (5 x) = 2

Divide both sides by

3

\frac{3 cos ( 5 x )}{3} = \frac{2}{3}

Simplify

cos (5 x) = \frac{2}{3}

cos (5 x) = \frac{2}{3}

Apply trig inverse properties

cos (5 x) = \frac{2}{3}

General solutions for

cos (5 x) = \frac{2}{3}

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

5 x = arccos (\frac{2}{3}) + 2 πn, 5 x = 2 π - arccos (\frac{2}{3}) + 2 πn

5 x = arccos (\frac{2}{3}) + 2 πn, 5 x = 2 π - arccos (\frac{2}{3}) + 2 πn

Solve

5 x = arccos (\frac{2}{3}) + 2 πn : x = \frac{arccos ( \frac{2}{3} )}{5} + \frac{2 πn}{5}

5 x = arccos (\frac{2}{3}) + 2 πn

Divide both sides by

5

5 x = arccos (\frac{2}{3}) + 2 πn

Divide both sides by

5

\frac{5 x}{5} = \frac{arccos ( \frac{2}{3} )}{5} + \frac{2 πn}{5}

Simplify

x = \frac{arccos ( \frac{2}{3} )}{5} + \frac{2 πn}{5}

x = \frac{arccos ( \frac{2}{3} )}{5} + \frac{2 πn}{5}

Solve

5 x = 2 π - arccos (\frac{2}{3}) + 2 πn : x = \frac{2 π}{5} - \frac{arccos ( \frac{2}{3} )}{5} + \frac{2 πn}{5}

5 x = 2 π - arccos (\frac{2}{3}) + 2 πn

Divide both sides by

5

5 x = 2 π - arccos (\frac{2}{3}) + 2 πn

Divide both sides by

5

\frac{5 x}{5} = \frac{2 π}{5} - \frac{arccos ( \frac{2}{3} )}{5} + \frac{2 πn}{5}

Simplify

x = \frac{2 π}{5} - \frac{arccos ( \frac{2}{3} )}{5} + \frac{2 πn}{5}

x = \frac{2 π}{5} - \frac{arccos ( \frac{2}{3} )}{5} + \frac{2 πn}{5}

x = \frac{arccos ( \frac{2}{3} )}{5} + \frac{2 πn}{5}, x = \frac{2 π}{5} - \frac{arccos ( \frac{2}{3} )}{5} + \frac{2 πn}{5}

Show solutions in decimal form

x = \frac{0.84106 \dots}{5} + \frac{2 πn}{5}, x = \frac{2 π}{5} - \frac{0.84106 \dots}{5} + \frac{2 πn}{5}

2 sin^{2} (θ) + cos (θ) - 1 = 0

3 sin^{2} (x) + sin (x) - 2 = 0

6 sin^{2} (θ) - sin (θ) - 2 = 0, 0 \leq θ \leq 2 π

33 cot (x) = 3

2 tan^{2} (x) - 6 = 0

What is the general solution for 3cos(5x)=2 ?
The general solution for 3cos(5x)=2 is x=(0.84106…)/5+(2pin)/5 ,x=(2pi)/5-(0.84106…)/5+(2pin)/5