What is the general solution for 7cos(5x)=6 ?

The general solution for 7cos(5x)=6 is x=(0.54109…)/5+(2pin)/5 ,x=(2pi)/5-(0.54109…)/5+(2pin)/5

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7cos(5x)=6

7 cos (5 x) = 6

x = \frac{0.54109 \dots}{5} + \frac{2 πn}{5}, x = \frac{2 π}{5} - \frac{0.54109 \dots}{5} + \frac{2 πn}{5}

Solution steps

7 cos (5 x) = 6

Divide both sides by

7

cos (5 x) = \frac{6}{7}

Apply trig inverse properties

5 x = arccos (\frac{6}{7}) + 2 πn, 5 x = 2 π - arccos (\frac{6}{7}) + 2 πn

Solve

5 x = arccos (\frac{6}{7}) + 2 πn : x = \frac{arccos ( \frac{6}{7} )}{5} + \frac{2 πn}{5}

Solve

5 x = 2 π - arccos (\frac{6}{7}) + 2 πn : x = \frac{2 π}{5} - \frac{arccos ( \frac{6}{7} )}{5} + \frac{2 πn}{5}

x = \frac{arccos ( \frac{6}{7} )}{5} + \frac{2 πn}{5}, x = \frac{2 π}{5} - \frac{arccos ( \frac{6}{7} )}{5} + \frac{2 πn}{5}

Show solutions in decimal form

x = \frac{0.54109 \dots}{5} + \frac{2 πn}{5}, x = \frac{2 π}{5} - \frac{0.54109 \dots}{5} + \frac{2 πn}{5}

3 sin (x) = 3 tan (x)

3 cos (11 θ) = 0

cos (2 a) = - 1

cos^{2} (θ) - 6 cos (θ) + 1 = 0

4 = 6 sec (x)

What is the general solution for 7cos(5x)=6 ?
The general solution for 7cos(5x)=6 is x=(0.54109…)/5+(2pin)/5 ,x=(2pi)/5-(0.54109…)/5+(2pin)/5