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

The value of cos((3pi)/2)cos(pi)-sin((3pi)/2)sin(pi) is 0

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cos((3pi)/2)cos(pi)-sin((3pi)/2)sin(pi)

cos (\frac{3 π}{2}) cos (π) - sin (\frac{3 π}{2}) sin (π)

0

Solution steps

cos (\frac{3 π}{2}) cos (π) - sin (\frac{3 π}{2}) sin (π)

Rewrite using trig identities:

cos (\frac{π}{2})

cos (\frac{3 π}{2}) cos (π) - sin (\frac{3 π}{2}) sin (π)

Use the Angle Sum identity:

cos (s) cos (t) - sin (s) sin (t) = cos (s + t)

= cos (\frac{3 π}{2} + π)

Simplify:

\frac{3 π}{2} + π = \frac{5 π}{2}

\frac{3 π}{2} + π

Convert element to fraction:

π = \frac{π 2}{2}

= \frac{3 π}{2} + \frac{π 2}{2}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{3 π + π 2}{2}

Add similar elements:

3 π + 2 π = 5 π

= \frac{5 π}{2}

= cos (\frac{5 π}{2})

cos (\frac{5 π}{2}) = cos (\frac{π}{2})

cos (\frac{5 π}{2})

Rewrite

\frac{5 π}{2}

2 π + \frac{π}{2}

= cos (2 π + \frac{π}{2})

Apply the periodicity of

cos

cos (x + 2 π) = cos (x)

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

= cos (\frac{π}{2})

= cos (\frac{π}{2})

= cos (\frac{π}{2})

Use the following trivial identity:

cos (\frac{π}{2}) = 0

cos (\frac{π}{2})

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 0

= 0

\frac{2 - 2 + 2 cos ( 8 0 ^{\circ} )}{sin ( 4 0 ^{\circ} )}

\frac{4}{sin ( 3 5 ^{\circ} )}

arctan (\frac{- 3.43}{1.1})

14 \cdot (cos (2 4^{\circ}))

- \frac{14 π}{3} sin (\frac{2 π ^{2.3} + 4 π}{3})

What is the value of cos((3pi)/2)cos(pi)-sin((3pi)/2)sin(pi) ?
The value of cos((3pi)/2)cos(pi)-sin((3pi)/2)sin(pi) is 0