What is the value of -11cos(pi/6*42)+12 ?

The value of -11cos(pi/6*42)+12 is 23

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-11cos(pi/6*42)+12

- 11 cos (\frac{π}{6} \cdot 42) + 12

23

Solution steps

- 11 cos (\frac{π}{6} \cdot 42) + 12

Simplify:

\frac{π}{6} \cdot 42 = 7 π

\frac{π}{6} \cdot 42

Multiply fractions:

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

= \frac{π 42}{6}

Divide the numbers:

\frac{42}{6} = 7

= 7 π

= - 11 cos (7 π) + 12

cos (7 π) = cos (π)

cos (7 π)

Rewrite

7 π

2 π \cdot 3 + π

= cos (2 π 3 + π)

Apply the periodicity of

cos

cos (x + 2 π \cdot k) = cos (x)

cos (2 π \cdot 3 + π) = cos (π)

= cos (π)

= - 11 cos (π) + 12

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)

= - 11 (- 1) + 12

Simplify

= 23

600 \cdot cos (6 0^{\circ})

tan (\frac{1}{6} π)

cos (2.25)

sin (\frac{π}{4}) - \frac{π}{4}

sin^{5} (- \frac{π}{2})