What is the value of 12-40pi^2cos(pi*6) ?

The value of 12-40pi^2cos(pi*6) is 12-40pi^2

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12-40pi^2cos(pi*6)

12 - 40 π^{2} cos (π \cdot 6)

12 - 40 π^{2}

Decimal Notation

- 382.78417 \dots

Solution steps

12 - 40 π^{2} cos (π 6)

Rewrite using trig identities:

cos (π 6) = 1

cos (π 6)

cos (π 6) = cos (0)

cos (π 6)

Rewrite

π 6

2 π \cdot 3 + 0

= cos (2 π 3 + 0)

Apply the periodicity of

cos

cos (x + 2 π \cdot k) = cos (x)

cos (2 π \cdot 3 + 0) = cos (0)

= cos (0)

= cos (0)

Use the following trivial identity:

cos (0) = 1

cos (0)

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

= 12 - 40 π^{2} \cdot 1

Simplify

= 12 - 40 π^{2}

π - arctan (\frac{3}{2})

\frac{8}{cos ( 4 5 ^{\circ} )}

sin (6 0^{\circ}) (8)

sin (1.9)

sec (- 63 0^{\circ})

What is the value of 12-40pi^2cos(pi*6) ?
The value of 12-40pi^2cos(pi*6) is 12-40pi^2