What is the value of -10cos(pi/6*39)+11 ?

The value of -10cos(pi/6*39)+11 is 11

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-10cos(pi/6*39)+11

- 10 cos (\frac{π}{6} \cdot 39) + 11

11

Solution steps

- 10 cos (\frac{π}{6} \cdot 39) + 11

Simplify:

\frac{π}{6} \cdot 39 = \frac{13 π}{2}

\frac{π}{6} \cdot 39

Multiply fractions:

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

= \frac{π 39}{6}

Cancel the common factor:

3

= \frac{13 π}{2}

= - 10 cos (\frac{13 π}{2}) + 11

cos (\frac{13 π}{2}) = cos (\frac{π}{2})

cos (\frac{13 π}{2})

Rewrite

\frac{13 π}{2}

2 π \cdot 3 + \frac{π}{2}

= cos (2 π 3 + \frac{π}{2})

Apply the periodicity of

cos

cos (x + 2 π \cdot k) = cos (x)

cos (2 π \cdot 3 + \frac{π}{2}) = cos (\frac{π}{2})

= cos (\frac{π}{2})

= - 10 cos (\frac{π}{2}) + 11

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

= - 10 \cdot 0 + 11

Simplify

= 11

cos (3 5^{\circ}) \cdot 420

100 cos (5 0^{\circ})

(sin (6))^{2}

cos^{2} (\frac{4.12 π}{6})

2 \cdot sec (\frac{π}{4})