What is the general solution for 0.87=5cos(3x) ?

The general solution for 0.87=5cos(3x) is x=(1.39590…)/3+(2pin)/3 ,x=(2pi)/3-(1.39590…)/3+(2pin)/3

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0.87=5cos(3x)

0.87 = 5 cos (3 x)

x = \frac{1.39590 \dots}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{1.39590 \dots}{3} + \frac{2 πn}{3}

Degrees

x = 26.65984 \dots^{\circ} + 12 0^{\circ} n, x = 93.34015 \dots^{\circ} + 12 0^{\circ} n

Solution steps

0.87 = 5 cos (3 x)

Switch sides

5 cos (3 x) = 0.87

Divide both sides by

5

5 cos (3 x) = 0.87

Divide both sides by

5

\frac{5 cos ( 3 x )}{5} = \frac{0.87}{5}

Simplify

cos (3 x) = 0.174

cos (3 x) = 0.174

Apply trig inverse properties

cos (3 x) = 0.174

General solutions for

cos (3 x) = 0.174

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

3 x = arccos (0.174) + 2 πn, 3 x = 2 π - arccos (0.174) + 2 πn

3 x = arccos (0.174) + 2 πn, 3 x = 2 π - arccos (0.174) + 2 πn

Solve

3 x = arccos (0.174) + 2 πn : x = \frac{arccos ( 0.174 )}{3} + \frac{2 πn}{3}

3 x = arccos (0.174) + 2 πn

Divide both sides by

3

3 x = arccos (0.174) + 2 πn

Divide both sides by

3

\frac{3 x}{3} = \frac{arccos ( 0.174 )}{3} + \frac{2 πn}{3}

Simplify

x = \frac{arccos ( 0.174 )}{3} + \frac{2 πn}{3}

x = \frac{arccos ( 0.174 )}{3} + \frac{2 πn}{3}

Solve

3 x = 2 π - arccos (0.174) + 2 πn : x = \frac{2 π}{3} - \frac{arccos ( 0.174 )}{3} + \frac{2 πn}{3}

3 x = 2 π - arccos (0.174) + 2 πn

Divide both sides by

3

3 x = 2 π - arccos (0.174) + 2 πn

Divide both sides by

3

\frac{3 x}{3} = \frac{2 π}{3} - \frac{arccos ( 0.174 )}{3} + \frac{2 πn}{3}

Simplify

x = \frac{2 π}{3} - \frac{arccos ( 0.174 )}{3} + \frac{2 πn}{3}

x = \frac{2 π}{3} - \frac{arccos ( 0.174 )}{3} + \frac{2 πn}{3}

x = \frac{arccos ( 0.174 )}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{arccos ( 0.174 )}{3} + \frac{2 πn}{3}

Show solutions in decimal form

x = \frac{1.39590 \dots}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{1.39590 \dots}{3} + \frac{2 πn}{3}

cos (\frac{2 π x}{3}) = \frac{1}{2}

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

\frac{1}{2} = cos (2 x)

- 1 + tan (x) = sec (x)

sin (\frac{x}{2}) = sin (2 x)

What is the general solution for 0.87=5cos(3x) ?
The general solution for 0.87=5cos(3x) is x=(1.39590…)/3+(2pin)/3 ,x=(2pi)/3-(1.39590…)/3+(2pin)/3