math and advance Trigonometry?

cos2A = 1 - 2sin²A

so cos4y = 1- 2sin²(2y)

Your equation becomes

sin2y = 1 - 2sin²(2y)

This is a quadratic, think of sin2y = s

2s² + s - 1 = 0

(2s -1)(s + 1) = 0

s = ½ or s = -1

sin2y = ½ or sin 2y = -1

2y = 30° , 150° , 390° , 510° ... or 2y = 270° , 630° ,.....

y = 15° , 75° , 195° , 255° or y = 135° , 315° where 0° < y < 360°.

sin2y = cos4y

= cos(2x2y)

= 1 - 2(sin2y)^2

=> 2(sin2y)^2 + sin2y - 1 = 0

This is a quadratic in terms of sin2y. If you dont see this then let sin2y=a, then

2a^2 + a -1 =0

(2a + 1)(a - 1) = 0

a = -0.5 or a = 1. Therefore:

sin2y = -0.5 or sin2y = 1

You should be able to solve that yourself, I'm not going to do all your work.

cos 4y= 1-2(sin2y)^2

substitute sin2y = 1-2(sin2y)^2

2(sin2y)^2 + sin2y -1=0

(sin2y+1)(2sin2y-1)=0

sin2y = -1 or sin2y = 1/2

2y = 270,630 or 2y =30 , 150,390,510

y = 135, 315 , 15 , 75 , 195, 225

Hi,

Graphing calculators are a wonderful thing.

Graph Y1 = sin(2x) and Y2 = cos(4x). Make window xmin = 0, xmax = 360, ymin = -2 and ymax = 2. Then graph and find intersections.

y = 15, 75, 135, 195, 255, and 315

I hope that helps!! :-)

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y = 45/2, 135/2, 225/2, 315/2.

It helps to make the substitution 2y = a, plot sin(a) and cos(2a) and graphically see at what values of 'a' they intersect.

Then solve for y.