What is the value of sec^2(pi/3)*(-0.1) ?

The value of sec^2(pi/3)*(-0.1) is -2/5

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sec^2(pi/3)*(-0.1)

sec^{2} (\frac{π}{3}) \cdot (- 0.1)

- \frac{2}{5}

Decimal Notation

- 0.4

Solution steps

sec^{2} (\frac{π}{3}) (- 0.1)

= sec^{2} (\frac{π}{3}) (- \frac{1}{10})

Use the following trivial identity:

sec (\frac{π}{3}) = 2

sec (\frac{π}{3})

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= 2

= 2^{2} (- \frac{1}{10})

Simplify

2^{2} (- \frac{1}{10}) : - \frac{2}{5}

2^{2} (- \frac{1}{10})

Remove parentheses:

(- a) = - a

= - 2^{2} \cdot \frac{1}{10}

Multiply fractions:

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

= - \frac{1 \cdot 2 ^{2}}{10}

Multiply:

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

= - \frac{2 ^{2}}{10}

Cancel

\frac{2 ^{2}}{10} : \frac{2}{5}

\frac{2 ^{2}}{10}

Factor

10 : 2 \cdot 5

Factor

10 = 2 \cdot 5

= \frac{2 ^{2}}{2 \cdot 5}

Cancel the common factor:

2

= \frac{2}{5}

= - \frac{2}{5}

= - \frac{2}{5}

200 \cdot cos (3 0^{\circ})

arctan (tan (π))

tan (- 0.5)

sec (\frac{15 π}{4})

20 cos (4 0^{\circ})

What is the value of sec^2(pi/3)*(-0.1) ?
The value of sec^2(pi/3)*(-0.1) is -2/5