Is sin(-pi/4)=-sin(pi/4) ?

The answer to whether sin(-pi/4)=-sin(pi/4) is True

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prove sin(-pi/4)=-sin(pi/4)

prove

sin (- \frac{π}{4}) = - sin (\frac{π}{4})

True

Solution steps

sin (- \frac{π}{4}) = - sin (\frac{π}{4})

Manipulating left side

sin (- \frac{π}{4})

Use the negative angle identity:

sin (- x) = - sin (x)

= - sin (\frac{π}{4})

We showed that the two sides could take the same form

\Rightarrow True

1 - 2 sin^{4} (x) = 1 - 2 sin^{2} (x)

sin (z + w) = sin (z) cos (w) + cos (z) sin (w)

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

sin (2 x) = 2 sin (x)

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