Trig Circular Functions part 21

Louise Johnson

Junior Member
Joined
Jan 21, 2007
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103
Hello could anyone give these a quick check? I realize these answers can be proven by plugging them in for x and verifying both sides are equal. However I have an incredible ability to miss stuff or just screw things up.
Thank you
Louise


Solve each equation for x where x is equal or greater than zero and less than 2pi

#1
Sinx=sqrt3cosx

Answer x=Pi/3 and 4pi/3

#2
Sin(x-pi/2)=cos^2x

Answer x= pi/2 and 3pi/2

#3 Prove the identity Find the exact value of cos 75degrees

Answer cos75degrees =cos(45+30)=cos45+30-sin45sin30
=sqrt6-sqrt2 over 4
 
sinx = sqrt3 cosx
tan x = sqrt3
sketch a right triangle , opposite side= sqrt3 adjacent side =1
then hypoteneuse = sqrt[3+1] = 2
cos x = 1/2
x=60 degrees
==========================================
sin[x-pi/2]=cos^2x
sin x cospi/2-cosx sin pi/2=cos^2x
-cosx=cos^2x
cos^2x+cosx=0
cosx[cosx+1]=0
cosx=0 or cosx=-1
x=90,270,180 degrees
but 90 is a invalid value

180 and 270 answer
=============================================
cos 75 = cos[45+30]
cos 75 = cos45 cos30 - sin45 sin30
cos75= [1/sqrt2][sqrt3/2] - [1/sqrt2][1/2]
cos 75=[sqrt3-1][2sqrt2]
cos76= 1/4[sqrt6-sqrt2]

Arthur
 
Thank you for your help. I managed to get one correct which is a good feeling. However on my other two questions I had thought I had them correct and even checked to make sure by plugging in the values for x which worked!!. However I think it was my algebra that let me down.
Thank you again
Louise
 
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