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# Identities and trig help

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Moderators, i know this is much, but i need this, i just got back from my finals and got a 100/126 on my finals, so i got a 88%percent on my onlinehomework, so i need help with these so that i could get 90.

Veteran  Mar 21, 2017
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y = 4x^2

rsin(theta)   = 4r^2cos^2 (theta)     divide by r on both sides

sin(theta)  = 4r * cos^2(theta)

r  = (1/4)sin(theta) / [cos^2 (theta) ]

r =  (1/4) sin(theta)/cos(theta) *  1 /cos(theta)

r =  (1/ 4) tan(theta) * sec(theta)

Look at the graph, here :  https://www.desmos.com/calculator/7uoqlyx4rx

sin^2(w)  - cos^2(w)   = sin(w) - 1

sin^2(w) - (1 - sin^2(w) )  - sin(w) + 1   =  0

2sin^2(w) - sin(w)   = 0         factor out a sin(w)

sin(w)  [ 2sin(w)  - 1 ]    = 0

So   either   .....   sin(w)   = 0  and this happens at 0  and pi     .....or....

2sin(w)  -  1   = 0       add 1

2sin(w)   =  1           divide by 2

sin(w)  = 1/2        and this happens at  pi/6 and 5pi/6

So   the solutions are   [ 0, pi/6, 5pi/6 , pi ]

Here's a graph of the solutions......https://www.desmos.com/calculator/c0wjnrrb0u

CPhill  Mar 21, 2017