What is the value of cos(3pi)-1 ?

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cos(3pi)-1

cos (3 π) - 1

- 2

Solution steps

cos (3 π) - 1

Rewrite using trig identities:

cos (3 π) = - 1

cos (3 π)

cos (3 π) = cos (π)

cos (3 π)

Rewrite

3 π

2 π + π

= cos (2 π + π)

Apply the periodicity of

cos

cos (x + 2 π) = cos (x)

cos (2 π + π) = cos (π)

= cos (π)

= cos (π)

Use the following trivial identity:

cos (π) = (- 1)

cos (π)

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}

= (- 1)

= - 1

= - 1 - 1

Simplify

= - 2

\frac{36}{2.8665600000000 \dots} sin (0.0478800000000 \dots)

sin (arcsin (\frac{5}{3} π))

22 cos (\frac{7 π}{4})

\frac{sin ( 3 \cdot ( - 0.1 ) )}{- 0.1}

\frac{3}{sin ( 3 6 ^{\circ} )}