What is the inverse of 2cos(2pi(x+(2pi)/3))-5 ?

The inverse of 2cos(2pi(x+(2pi)/3))-5 is (arccos((x+5)/2))/(2pi)-(2pi)/3

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inverse of 2cos(2pi(x+(2pi)/3))-5

inverse

2 cos (2 π (x + \frac{2 π}{3})) - 5

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

Solution steps

Solve for

cos (2 π (x + \frac{2 π}{3})), y = 2 cos (2 π (x + \frac{2 π}{3})) - 5

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

cos (a) = b \Rightarrow a = arccos (b)

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

Solve for

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

\frac{arccos ( \frac{y + 5}{2} )}{2 π} - \frac{2 π}{3}

Substitute

y = x

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

f (x) = \frac{3 - x}{x}

f (x) = x^{(- \frac{3}{2})}

\frac{25}{10} \frac{15}{x}

f (x) = 3 x + 11 + 12

x = 0.4 t + 6.6

What is the inverse of 2cos(2pi(x+(2pi)/3))-5 ?
The inverse of 2cos(2pi(x+(2pi)/3))-5 is (arccos((x+5)/2))/(2pi)-(2pi)/3