Is sin(pi)=sin(-pi) ?

The answer to whether sin(pi)=sin(-pi) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove sin(pi)=sin(-pi)

prove

sin (π) = sin (- π)

True

Solution steps

sin (π) = sin (- π)

Manipulating left side

sin (π)

Simplify

= 0

Manipulating right side

sin (- π)

Use the negative angle identity:

sin (- x) = - sin (x)

= - sin (π)

Simplify

- sin (π) : 0

- sin (π)

Use the following trivial identity:

sin (π) = 0

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

= 0

= 0

We showed that the two sides could take the same form

\Rightarrow True

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

csc (t) cot (t) = \frac{1 + cot ^{2} ( t )}{sec ( t )}

csc (a) sec (a) = 2 csc (2 a)

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

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