What is the value of sqrt(7+sec^2(0)) ?

The value of sqrt(7+sec^2(0)) is 2sqrt(2)

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sqrt(7+sec^2(0))

7 + sec^{2} (0)

22

Decimal Notation

2.82842 \dots

Solution steps

7 + sec^{2} (0)

Use the following trivial identity:

sec (0) = 1

sec (0)

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}

= 1

= 7 + 1^{2}

Simplify

7 + 1^{2} : 22

7 + 1^{2}

Apply rule

1^{a} = 1

1^{2} = 1

= 7 + 1

Add the numbers:

7 + 1 = 8

= 8

Prime factorization of

8 : 2^{3}

8

8

divides by

28 = 4 \cdot 2

= 2 \cdot 4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2 \cdot 2

2

is a prime number, therefore no further factorization is possible

= 2 \cdot 2 \cdot 2

= 2^{3}

= 2^{3}

Apply exponent rule:

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

= 2^{2} \cdot 2

Apply radical rule:

= 2 2^{2}

Apply radical rule:

2^{2} = 2

= 22

= 22

3^{c o s (5 + 5)} + 1

1 - cos^{2} (\frac{9 π}{8})

tan (arccos (\frac{12}{20}))

sec^{2} (- 0.01)

6 sin (\frac{π}{4}) - cos (\frac{π}{4})

What is the value of sqrt(7+sec^2(0)) ?
The value of sqrt(7+sec^2(0)) is 2sqrt(2)