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

The value of sec(-(7pi)/2) is Undefined

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sec(-(7pi)/2)

sec (- \frac{7 π}{2})

Undefined

Solution steps

sec (- \frac{7 π}{2})

Use the following property:

sec (- x) = sec (x)

sec (- \frac{7 π}{2}) = sec (\frac{7 π}{2})

= sec (\frac{7 π}{2})

sec (\frac{7 π}{2}) = sec (\frac{3 π}{2})

sec (\frac{7 π}{2})

Rewrite

\frac{7 π}{2}

2 π + \frac{3 π}{2}

= sec (2 π + \frac{3 π}{2})

Apply the periodicity of

sec

sec (x + 2 π) = sec (x)

sec (2 π + \frac{3 π}{2}) = sec (\frac{3 π}{2})

= sec (\frac{3 π}{2})

= sec (\frac{3 π}{2})

Rewrite using trig identities:

Undefined

sec (\frac{3 π}{2})

Use the basic trigonometric identity:

sec (x) = \frac{1}{cos ( x )}

= \frac{1}{cos ( \frac{3 π}{2} )}

Simplify

\frac{1}{cos ( \frac{3 π}{2} )} :

Undefined

\frac{1}{cos ( \frac{3 π}{2} )}

cos (\frac{3 π}{2}) = 0

= \frac{1}{0}

\frac{x}{0}

is undefined

= Undefined

= Undefined

= Undefined

\frac{10}{sin ( 4 5 ^{\circ} )}

9 sin (7 5^{\circ})

sin (arcsin (- 1))

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

arctan (\frac{2}{5})