Author Topic: cosec intercept question (Read 947 times) Tweet Share

JackSonSmith · « **on:** January 03, 2015, 08:58:54 pm »

Sketch the graph of each of the following, over the interval [0, 2pi]:
y = cosec ( x + pi / 4 )

I'm getting root 2 / 2 for the y intercept yet the book says its just root 2. Could someone please explain how to find the y intercept.

IndefatigableLover · « **Reply #1 on:** January 03, 2015, 10:11:58 pm »

Quote from: JackSonSmith on January 03, 2015, 08:58:54 pm

Sketch the graph of each of the following, over the interval [0, 2pi]:
y = cosec ( x + pi / 4 )

I'm getting root 2 / 2 for the y intercept yet the book says its just root 2. Could someone please explain how to find the y intercept.

If you sub x=0 into $y=\csc(x+\frac{\pi}{4})$ , you'll end up with:

$y=\csc(\frac{\pi}{4})$ (Expand it out and we get):

You know that cosec is the same as 1/sin so another way of writing this is:

$y=\frac{1}{\sin(\frac{\pi}{4})}$

$y=\frac{1}{\frac{\sqrt{2}}{2}}$

$y=\frac{2}{\sqrt{2}}$

You can leave your answer like that since in Specialist you don't need to rationalise but if you do then it'll equal $\sqrt{2}$

JackSonSmith · « **Reply #2 on:** January 09, 2015, 05:40:18 pm »

Could you please explain how 2 / root2 becomes root2

Conic · « **Reply #3 on:** January 09, 2015, 05:43:59 pm »

Rationalise the denominator:

$\frac{2}{\sqrt{2}}=\frac{2}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}=\frac{2\sqrt{2}}{(\sqrt{2})^2}=\frac{2\sqrt{2}}{2}=\sqrt{2}.$

JackSonSmith · « **Reply #4 on:** January 09, 2015, 08:26:34 pm »

Thank-you both for your help.

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