What is the inverse of 2cos((2pit)/3) ?

The inverse of 2cos((2pit)/3) is (3arccos(t/2))/(2pi)

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inverse of 2cos((2pit)/3)

inverse

2 cos (\frac{2 π t}{3})

\frac{3 arccos ( \frac{t}{2} )}{2 π}

Solution steps

Solve for

cos (\frac{2 π t}{3}), y = 2 cos (\frac{2 π t}{3})

cos (\frac{2 π t}{3}) = \frac{y}{2}

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

\frac{2 π t}{3} = arccos (\frac{y}{2})

Solve for

t, \frac{2 π t}{3} = arccos (\frac{y}{2})

\frac{3 arccos ( \frac{y}{2} )}{2 π}

Substitute

y = t

\frac{3 arccos ( \frac{t}{2} )}{2 π}

f (x) = lo g_{\frac{1}{2}} (2 y) + 3

f (x) = \frac{( 4 x - 7 )}{2 x + 3}

f (x) = 0.5 x - 5

f (x) = (1 + x) x

What is the inverse of 2cos((2pit)/3) ?
The inverse of 2cos((2pit)/3) is (3arccos(t/2))/(2pi)