What is the value of sin((27pi)/2) ?

The value of sin((27pi)/2) is -1

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sin((27pi)/2)

sin (\frac{27 π}{2})

- 1

Solution steps

sin (\frac{27 π}{2})

sin (\frac{27 π}{2}) = sin (\frac{3 π}{2})

= sin (\frac{3 π}{2})

Rewrite using trig identities:

sin (π) cos (\frac{π}{2}) + cos (π) sin (\frac{π}{2})

= sin (π) cos (\frac{π}{2}) + cos (π) sin (\frac{π}{2})

Use the following trivial identity:

sin (π) = 0

Use the following trivial identity:

cos (\frac{π}{2}) = 0

Use the following trivial identity:

cos (π) = (- 1)

Use the following trivial identity:

sin (\frac{π}{2}) = 1

= 0 \cdot 0 + (- 1) \cdot 1

Simplify

= - 1

arctan (\infty) - arctan (- \infty)

1 + cos (\frac{π}{4})

10 sin (3 7^{\circ})

\frac{6}{sin ( 6 0 ^{\circ} )}

cos (\frac{11 π}{2})