What is the value of sin(7*pi/2) ?

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sin(7*pi/2)

sin (7 \cdot \frac{π}{2})

- 1

Solution steps

sin (7 \cdot \frac{π}{2})

Simplify:

7 \cdot \frac{π}{2} = \frac{7 π}{2}

= sin (\frac{7 π}{2})

sin (\frac{7 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

csc (\frac{2}{2})

sin (- 0.6)

8 cos (27 0^{\circ})

cos^{2} (3 3^{\circ})

2 sin (\frac{π}{4}) 2 cos (\frac{π}{4})