What is the value of sec^2((7pi)/4) ?

The value of sec^2((7pi)/4) is 2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sec^2((7pi)/4)

sec^{2} (\frac{7 π}{4})

2

Solution steps

sec^{2} (\frac{7 π}{4})

Rewrite using trig identities:

tan^{2} (\frac{3 π}{4}) + 1

sec^{2} (\frac{7 π}{4})

Use the Pythagorean identity:

sec^{2} (x) = tan^{2} (x) + 1

= tan^{2} (\frac{7 π}{4}) + 1

tan (\frac{7 π}{4}) = tan (\frac{3 π}{4})

tan (\frac{7 π}{4})

Rewrite

\frac{7 π}{4}

π + \frac{3 π}{4}

= tan (π + \frac{3 π}{4})

Apply the periodicity of

tan

tan (x + π) = tan (x)

tan (π + \frac{3 π}{4}) = tan (\frac{3 π}{4})

= tan (\frac{3 π}{4})

= tan^{2} (\frac{3 π}{4}) + 1

= tan^{2} (\frac{3 π}{4}) + 1

Rewrite using trig identities:

sec^{2} (\frac{3 π}{4})

tan^{2} (\frac{3 π}{4}) + 1

Use the Pythagorean identity:

tan^{2} (x) + 1 = sec^{2} (x)

= sec^{2} (\frac{3 π}{4})

= sec^{2} (\frac{3 π}{4})

Use the following trivial identity:

sec (\frac{3 π}{4}) = - 2

sec (\frac{3 π}{4})

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} : 2

(- 2)^{2}

Apply exponent rule:

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

n

is even

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

= (2)^{2}

Apply radical rule:

a = a^{\frac{1}{2}}

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

Apply exponent rule:

(a^{b})^{c} = a^{b c}

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

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

Multiply fractions:

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

= \frac{1 \cdot 2}{2}

Cancel the common factor:

2

= 1

= 2

= 2

arccosh (\frac{5}{4})

- 8.4 \cdot cos (11 0^{\circ})

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

5 \cdot arctan (12 0^{\circ})

arcsin (0.44125)