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Popular >

cos(3pi)

Solution

cos (3 π)

Solution

- 1

Solution steps

cos (3 π)

cos (3 π) = cos (π)

cos (3 π)

Rewrite

3 π

as

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

Popular Examples

8sin^2(x)+2cos(x)=7

8 sin^{2} (x) + 2 cos (x) = 7

tan((19pi)/(12))

tan (\frac{19 π}{12})

prove 1/(sec(x)-tan(x))=sec(x)+tan(x)prove

\frac{1}{sec ( x ) - tan ( x )} = sec (x) + tan (x)

cos (9 0^{\circ})

cos (- \frac{3 π}{4})

Frequently Asked Questions (FAQ)

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