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Popular >

7cos(3x)=2,0<= x<2pi

Solution

7 cos (3 x) = 2, 0 \leq x < 2 π

Solution

x = \frac{1.28104 \dots}{3}, x = \frac{2 π - 1.28104 \dots}{3}, x = \frac{1.28104 \dots + 2 π}{3}, x = \frac{4 π - 1.28104 \dots}{3}, x = \frac{1.28104 \dots + 4 π}{3}, x = \frac{6 π - 1.28104 \dots}{3}

+1

Degrees

x = 24.46615 \dots^{\circ}, x = 95.53384 \dots^{\circ}, x = 144.46615 \dots^{\circ}, x = 215.53384 \dots^{\circ}, x = 264.46615 \dots^{\circ}, x = 335.53384 \dots^{\circ}

Solution steps

7 cos (3 x) = 2, 0 \leq x < 2 π

Divide both sides by

7

7 cos (3 x) = 2

Divide both sides by

7

\frac{7 cos ( 3 x )}{7} = \frac{2}{7}

Simplify

cos (3 x) = \frac{2}{7}

cos (3 x) = \frac{2}{7}

Apply trig inverse properties

cos (3 x) = \frac{2}{7}

General solutions for

cos (3 x) = \frac{2}{7}

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

3 x = arccos (\frac{2}{7}) + 2 πn, 3 x = 2 π - arccos (\frac{2}{7}) + 2 πn

3 x = arccos (\frac{2}{7}) + 2 πn, 3 x = 2 π - arccos (\frac{2}{7}) + 2 πn

Solve

3 x = arccos (\frac{2}{7}) + 2 πn : x = \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}

3 x = arccos (\frac{2}{7}) + 2 πn

Divide both sides by

3

3 x = arccos (\frac{2}{7}) + 2 πn

Divide both sides by

3

\frac{3 x}{3} = \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}

Simplify

x = \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}

x = \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}

Solve

3 x = 2 π - arccos (\frac{2}{7}) + 2 πn : x = \frac{2 π}{3} - \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}

3 x = 2 π - arccos (\frac{2}{7}) + 2 πn

Divide both sides by

3

3 x = 2 π - arccos (\frac{2}{7}) + 2 πn

Divide both sides by

3

\frac{3 x}{3} = \frac{2 π}{3} - \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}

Simplify

x = \frac{2 π}{3} - \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}

x = \frac{2 π}{3} - \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}

x = \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}

Solutions for the range

0 \leq x < 2 π

x = \frac{arccos ( \frac{2}{7} )}{3}, x = \frac{2 π - arccos ( \frac{2}{7} )}{3}, x = \frac{arccos ( \frac{2}{7} ) + 2 π}{3}, x = \frac{4 π - arccos ( \frac{2}{7} )}{3}, x = \frac{arccos ( \frac{2}{7} ) + 4 π}{3}, x = \frac{6 π - arccos ( \frac{2}{7} )}{3}

Show solutions in decimal form

x = \frac{1.28104 \dots}{3}, x = \frac{2 π - 1.28104 \dots}{3}, x = \frac{1.28104 \dots + 2 π}{3}, x = \frac{4 π - 1.28104 \dots}{3}, x = \frac{1.28104 \dots + 4 π}{3}, x = \frac{6 π - 1.28104 \dots}{3}

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