What is the general solution for 2cos(3x)= 1/2 ,x=(17pi)/4 ?

The general solution for 2cos(3x)= 1/2 ,x=(17pi)/4 is No Solution for x\in\mathbb{R}

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2cos(3x)= 1/2 ,x=(17pi)/4

2 cos (3 x) = \frac{1}{2}, x = \frac{17 π}{4}

No Solution for x \in R

Solution steps

2 cos (3 x) = \frac{1}{2}, x = \frac{17 π}{4}

Divide both sides by

2

2 cos (3 x) = \frac{1}{2}

Divide both sides by

2

\frac{2 cos ( 3 x )}{2} = \frac{\frac{1}{2}}{2}

Simplify

\frac{2 cos ( 3 x )}{2} = \frac{\frac{1}{2}}{2}

Simplify

\frac{2 cos ( 3 x )}{2} : cos (3 x)

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

Divide the numbers:

\frac{2}{2} = 1

= cos (3 x)

Simplify

\frac{\frac{1}{2}}{2} : \frac{1}{4}

\frac{\frac{1}{2}}{2}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{1}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{1}{4}

cos (3 x) = \frac{1}{4}

cos (3 x) = \frac{1}{4}

cos (3 x) = \frac{1}{4}

Apply trig inverse properties

cos (3 x) = \frac{1}{4}

General solutions for

cos (3 x) = \frac{1}{4}

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

3 x = arccos (\frac{1}{4}) + 2 πn, 3 x = 2 π - arccos (\frac{1}{4}) + 2 πn

3 x = arccos (\frac{1}{4}) + 2 πn, 3 x = 2 π - arccos (\frac{1}{4}) + 2 πn

Solve

3 x = arccos (\frac{1}{4}) + 2 πn : x = \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

3 x = arccos (\frac{1}{4}) + 2 πn

Divide both sides by

3

3 x = arccos (\frac{1}{4}) + 2 πn

Divide both sides by

3

\frac{3 x}{3} = \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

Simplify

x = \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

x = \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

Solve

3 x = 2 π - arccos (\frac{1}{4}) + 2 πn : x = \frac{2 π}{3} - \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

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

Divide both sides by

3

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

Divide both sides by

3

\frac{3 x}{3} = \frac{2 π}{3} - \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

Simplify

x = \frac{2 π}{3} - \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

x = \frac{2 π}{3} - \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

x = \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

Solutions for the range

x = \frac{17 π}{4}

No Solution for x \in R

cos (θ) = sin (3 6^{\circ})

2 sec^{2} (x) = tan^{2} (x) + 2 sec (x) + 4

cos^{2} (θ) + sin (θ) + 1 = 0

cos (x) = \frac{22.5}{34}

tan (x) = - \frac{6}{7}

What is the general solution for 2cos(3x)= 1/2 ,x=(17pi)/4 ?
The general solution for 2cos(3x)= 1/2 ,x=(17pi)/4 is No Solution for x\in\mathbb{R}