Use sum or difference identities to find the exact value of sin285

Question

Use sum or difference identities to find the exact value of sin285

in progress 0
Allison 2 weeks 2021-11-25T12:02:15+00:00 1 Answer 0

Answers ( )

    0
    2021-11-25T12:03:30+00:00

    Angle sum identity:

    \sin285^\circ=\sin(240^\circ+45^\circ)=\sin240^\circ\cos45^\circ+\cos240^\circ\sin45^\circ

    Now

    \sin240^\circ=\sin(180^\circ+60^\circ)=-\sin60^\circ=-\dfrac{\sqrt3}2

    \cos240^\circ=\cos(180^\circ+60^\circ)=-\cos60^\circ=-\dfrac12

    \sin45^\circ=\cos45^\circ=\dfrac1{\sqrt2}

    so we end up with

    \sin285^\circ=-\dfrac{\sqrt3}{2\sqrt2}-\dfrac1{2\sqrt2}=-\dfrac{\sqrt3+1}{2\sqrt2}=-\dfrac{\sqrt6+\sqrt2}4

Leave an answer

Browse
Browse

27:3+15-4x7+3-1=? ( )