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Popular >

sec^2((2pi)/3)

Solution

sec^{2} (\frac{2 π}{3})

Solution

4

Solution steps

sec^{2} (\frac{2 π}{3})

Use the following trivial identity:

sec (\frac{2 π}{3}) = - 2

sec (\frac{2 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}

Simplify

(- 2)^{2} : 4

(- 2)^{2}

Apply exponent rule:

(- a)^{n} = a^{n},

if

n

is even

(- 2)^{2} = 2^{2}

= 2^{2}

2^{2} = 4

= 4

= 4

Popular Examples

sin(pi/6)+cos(pi/6)

sin (\frac{π}{6}) + cos (\frac{π}{6})

sin (\frac{π}{7})

arccot (- 4)

2 cos (\frac{7 π}{4})

2 sin (\frac{3 π}{4})

Frequently Asked Questions (FAQ)

What is the value of sec^2((2pi)/3) ?
The value of sec^2((2pi)/3) is 4