Question

Какие из равенств верны ? а) sin40*=sin140* b) cos140*= - cos40* c) cos46*=cos134* d) sin130*=sin50* e) sin120*= - sin60* f) cos150*= - cos30*

Answer 1

Формулы приведения:
$\sin(180^\circ- \alpha )=\sin \alpha \\\ \cos(180^\circ- \alpha )=-\cos \alpha$

$\sin40^\circ=\sin140^\circ \\\ \sin(180^\circ-40^\circ)=\sin140^\circ \\\ \sin140^\circ=\sin140^\circ$
верно

$\cos140^\circ= - \cos40^\circ \\\ -\cos(180^\circ-140^\circ)= - \cos40^\circ \\\ -\cos40^\circ= - \cos40^\circ$
верно

$\cos46^\circ=\cos134^\circ \\\ -\cos(180^\circ-46^\circ)=\cos134^\circ \\\ -\cos134^\circ=\cos134^\circ$
неверно

$\sin130^\circ=\sin50^\circ \\\ \sin(180^\circ-130^\circ)=\sin50^\circ \\\ \sin50^\circ=\sin50^\circ$
верно

$\sin120^\circ= - \sin60^\circ \\\ \sin(180^\circ-120^\circ)= - \sin60^\circ \\\ \sin60^\circ= - \sin60^\circ$
неверно

$\cos150^\circ= - \cos30^\circ \\\ -\cos(180^\circ-150^\circ)= - \cos30^\circ \\\ -\cos30^\circ= - \cos30^\circ$
верно