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

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cos(pi/2*3)

cos (\frac{π}{2} \cdot 3)

0

Solution steps

cos (\frac{π}{2} \cdot 3)

Simplify:

\frac{π}{2} \cdot 3 = \frac{3 π}{2}

= cos (\frac{3 π}{2})

Rewrite using trig identities:

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

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

Use the following trivial identity:

cos (π) = (- 1)

Use the following trivial identity:

cos (\frac{π}{2}) = 0

Use the following trivial identity:

sin (π) = 0

Use the following trivial identity:

sin (\frac{π}{2}) = 1

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

Simplify

= 0

tan (3 0^{\circ}) \cdot cos (3 0^{\circ})

arctan (- 90)

1 - 2 sin^{2} (\frac{3 π}{5})

sin (2 π \cdot 2)

arccos (\frac{4}{32})