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

The value of sin((7pi)/2) is -1

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sin((7pi)/2)

sin (\frac{7 π}{2})

- 1

Solution steps

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

cos (\frac{π}{2})

2 sin (x) + 1 = 0

sin (- 3 0^{\circ})

cos^{2} (x) = 1

x, cos (2 x) = - \frac{3}{2}