What is expand-pisin(1/(2pi)(t-1)) ?

The solution to expand-pisin(1/(2pi)(t-1)) is -pisin((t-1)/(2pi))

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expand-pisin(1/(2pi)(t-1))

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- π sin (\frac{1}{2 π} (t - 1))

- π sin (\frac{t - 1}{2 π})

Solution steps

- π sin (\frac{1}{2 π} (t - 1))

Expand

\frac{1}{2 π} (t - 1) : \frac{1}{2 π} t - 1 \cdot \frac{1}{2 π}

= - π sin (\frac{1}{2 π} t - 1 \cdot \frac{1}{2 π})

Rewrite using trig identities

= - π (cos (\frac{1}{2 π}) sin (\frac{t}{2 π}) - sin (\frac{1}{2 π}) cos (\frac{t}{2 π}))

Use the Angle Difference identity:

sin (s) cos (t) - cos (s) sin (t) = sin (s - t)

= - π sin (\frac{t}{2 π} - \frac{1}{2 π})

Join

\frac{t}{2 π} - \frac{1}{2 π} : \frac{t - 1}{2 π}

= - π sin (\frac{t - 1}{2 π})

\frac{2 ( - 4 π - 9 )}{3 π}

ab - 9 a c + 3 b c + 9 b c - 2 a c + 3 ab

(1 + y + y^{2}) d x

\frac{1}{x ^{3} \cdot ( t - 1 ) ^{2}}

(4 - 2 ln (t))^{4}

What is expand-pisin(1/(2pi)(t-1)) ?
The solution to expand-pisin(1/(2pi)(t-1)) is -pisin((t-1)/(2pi))