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Note, you might want to simplify things a bit for the final answer, particularly in the numerators. For example, in #2, instead of x(7x) on the numerator you could write it as 7x^2 [^ meaning exponent]

Or in #3, instead of 1(x+2) you can simplify to x+2.

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riseandshinesammyy:

If someone could label the points for me I’ll love you forever

We need to know x when y=0

So… 0 = (5/3)sin(-2xπ/3) … 0/(5/3) = sin(-2xπ/3) … 0 = sin(-2xπ/3)

Let ϴ = -2xπ/3

Then … 0 = sin(ϴ)

From the unit circle we know ϴ = 0, -π, -2π for one negative rotation (if you use one positive rotation, you will still get correct axis labels, they will just be the negative x-axis labels)

Replace ϴ with -2xπ/3 and solve for x

ϴ = 0 …

-2xπ/3 = 0 … -2xπ = 0*3 … -2xπ = 0 … x = 0/(-2π) … x = 0

ϴ = -π…

-2xπ/3 = -π … -2xπ = -π*3 … -2xπ = -3π … x = -3π/(-2π) … x = 3/2

ϴ = -2π …

-2xπ/3 = -2π … -2xπ = -2π*3 … -2xπ = -6π … x = -6π/(-2π) … x = 3

So your axis labels are 0, 3/2, 3

(Source: hecklingxhoechlin)

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Disclaimer: I only vaguely remember learning about this once for about 5 minutes in a class I took 4 years ago… When I have more time I will try to confirm that it is correct.

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Also note that Chain Rule is being used throughout!