My Math Forum Unit circle problem!

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February 14th, 2012, 12:25 AM   #1
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Unit circle problem!

With the help of the unit circle, decide the exact value off:

cos?(90+v)+2cos?(180+v)

(Thx for any help!)
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 February 14th, 2012, 12:48 AM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs Re: Unit circle problem! Use the angle sum identity for cosine to state: $\cos$$90^{\circ}+v$$+2\cos$$180^{\circ}+v$$=$ $\cos$$90^{\circ}$$\cos(v)-\sin$$90^{\circ}$$\sin(v)+2$$\cos\(180^{\circ}$$\c os(v)-\sin$$180^{\circ}$$\sin(v)\)$ Since: $\cos$$90^{\circ}$$=0$ $\sin$$90^{\circ}$$=1$ $\cos$$180^{\circ}$$=-1$ $\sin$$180^{\circ}$$=0$ We have: $0\cdot\cos(v)-1\cdot\sin(v)+2$$-1\cdot\cos(v)-0\cdot\sin(v)$$=$ $-\sin(v)-2\cos(v)$ From the diagram, we see: $\sin(v)=0,8$ and $\cos(v)=0,6$ so we now have: $-0,8-2\cdot0,6=-2$ Another way to proceed would be to graphically add 90° to v and we the x-coordinate is -0.8. Then graphically add 180° to v and doubling the x-coordinate we get -1.2, and their sum is -2.

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