What is the value of csc^2((3pi)/2) ?

The value of csc^2((3pi)/2) is 1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

csc^2((3pi)/2)

csc^{2} (\frac{3 π}{2})

1

Solution steps

csc^{2} (\frac{3 π}{2})

Rewrite using trig identities:

1 + cot^{2} (\frac{π}{2})

csc^{2} (\frac{3 π}{2})

Use the Pythagorean identity:

csc^{2} (x) = 1 + cot^{2} (x)

= 1 + cot^{2} (\frac{3 π}{2})

cot (\frac{3 π}{2}) = cot (\frac{π}{2})

cot (\frac{3 π}{2})

Rewrite

\frac{3 π}{2}

π + \frac{π}{2}

= cot (π + \frac{π}{2})

Apply the periodicity of

cot

cot (x + π) = cot (x)

cot (π + \frac{π}{2}) = cot (\frac{π}{2})

= cot (\frac{π}{2})

= 1 + cot^{2} (\frac{π}{2})

= 1 + cot^{2} (\frac{π}{2})

Use the following trivial identity:

cot (\frac{π}{2}) = 0

cot (\frac{π}{2})

cot (x)

periodicity table with

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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

= 0

= 1 + 0^{2}

Simplify

= 1

\frac{cos ( 1 ) - 1}{1}

sin^{2} (2 3^{\circ})

sec (60 0^{\circ}) + cot (31 5^{\circ})

3 cos (0^{2}) - 18 (0)^{2} sin (0^{2}) - 8 (0)^{4} cos (0^{2})

sin (\frac{4}{5} - \frac{5}{13})