What is the value of sin(3 pi/2) ?

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sin(3 pi/2)

sin (3 \frac{π}{2})

- 1

Solution steps

sin (3 \cdot \frac{π}{2})

Simplify:

3 \cdot \frac{π}{2} = \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

50 sin (3 0^{\circ})

sin (- 4 π)

arcsec (6)

arcsin (- \frac{3}{4})

sin (\frac{π}{4}) - cos (\frac{π}{4})