What is the value of (picos(pi)-sin(pi))/(-pisin(pi)-cos(pi)) ?

The value of (picos(pi)-sin(pi))/(-pisin(pi)-cos(pi)) is -pi

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(picos(pi)-sin(pi))/(-pisin(pi)-cos(pi))

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

- π

Decimal Notation

- 3.14159 \dots

Solution steps

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

Use the following trivial identity:

cos (π) = (- 1)

cos (π)

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} 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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= (- 1)

Use the following trivial identity:

sin (π) = 0

sin (π)

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 0

= \frac{π ( - 1 ) - 0}{- π 0 - ( - 1 )}

Simplify

= - π

2 tan (\frac{π}{2})

sin (3 0^{\circ}) + sin (6 0^{\circ})

tan (4.5)

sin (3 0^{\circ}) csc (3 0^{\circ})

sec (- 4 π)

What is the value of (picos(pi)-sin(pi))/(-pisin(pi)-cos(pi)) ?
The value of (picos(pi)-sin(pi))/(-pisin(pi)-cos(pi)) is -pi