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Thanks.
Q3, it's right that cos(y)=4/5, but the next step is not right because it's not generally true that cos(2*theta) = 2*cos(theta).
Use identity $\displaystyle \cos(2y) = \cos^2(y)-\sin^2(y) = 2\cos^2(y)-1 = 2\cdot(4/5)^2-1 =\ ?$
Q1 You need to know interval notation to see what form the answer is supposed to be in. And as for getting the answer you can do:
$\displaystyle x^3+3x<4x^2 \ \ \ \iff$
$\displaystyle x^3-4x^2+3x < 0\ \ \ \iff$
$\displaystyle x(x^2-4x+3) < 0 \ \ \ \iff$
$\displaystyle \;?$
Factor the quadratic and see where the inequality holds.
Q2 asks you to find some trig function values based on a single given value. You need some trig identities. One such is that $\displaystyle \sin^2(\theta)+\cos^2(\theta)=1$. Can you continue?
$\displaystyle x^3- 4x^2+ 3x= x(x- 3)(x- 4)$
and a product of numbers is positive if and only if an even number of its factors are negative.
csc is defined as "hypotenuse over opposite side" so you can imagine a right triangle with one vertex at (0, 0) on a coordinate system, right angle at (3, 0) and hypotenus of length 5. Where is the third vertex?2.)
cos(2y)= cos^2(y)- sin^2(y). You are told what sin(y) is and, of course, cos(y)= 1/sec(y).3.)