If sin y = cos 3y, determine an exact value for angle y.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to find y such that sin y = cos 3y.

We know that sin(y) = cos(pi/2-y),so we can convert the given equation to:

sin(y) = cos(pi/2-y) = cos(3y)

We now equate pi/2 - y and 3y

pi/2 - y = 3y

=> pi/2 = 3y + y

=> 4y = pi/2

=> y = pi/8

Therefore y = pi/8 + 2*n*pi

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