What is the value of 6(6)^2-8+40cos(pi)(6) ?

The value of 6(6)^2-8+40cos(pi)(6) is -32

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6(6)^2-8+40cos(pi)(6)

6 (6)^{2} - 8 + 40 cos (π) (6)

- 32

Solution steps

6 (6)^{2} - 8 + 40 cos (π) (6)

= 6 \cdot 6^{2} - 8 + 40 cos (π) \cdot 6

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)

= 6 \cdot 6^{2} - 8 + 40 (- 1) \cdot 6

Simplify

6 \cdot 6^{2} - 8 + 40 (- 1) \cdot 6 : - 32

6 \cdot 6^{2} - 8 + 40 (- 1) \cdot 6

Remove parentheses:

(- a) = - a

= 6 \cdot 6^{2} - 8 - 40 \cdot 1 \cdot 6

6 \cdot 6^{2} = 6^{3}

6 \cdot 6^{2}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

6 \cdot 6^{2} = 6^{1 + 2}

= 6^{1 + 2}

Add the numbers:

1 + 2 = 3

= 6^{3}

40 \cdot 1 \cdot 6 = 240

40 \cdot 1 \cdot 6

Multiply the numbers:

40 \cdot 1 \cdot 6 = 240

= 240

= 6^{3} - 8 - 240

Subtract the numbers:

- 8 - 240 = - 248

= 6^{3} - 248

6^{3} = 216

= 216 - 248

Subtract the numbers:

216 - 248 = - 32

= - 32

= - 32

(sin (2))^{2}

1 - 2 cos (0)

3 sin (\frac{7 π}{4})

tan (\frac{5}{13})

300 \cdot sin (4 5^{\circ})

What is the value of 6(6)^2-8+40cos(pi)(6) ?
The value of 6(6)^2-8+40cos(pi)(6) is -32