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C3 Trigonometry.

x = Theta

(a) Sketch the graph of y=1+2secx in the interval −π ≤ θ ≤ 2π. (done)

(b) Write down the y-coordinate of points at which the gradient is zero. (done)

(c) Deduce the maximum and minimum values of 1/ 1+2secx and give the smallest positive values of θ at which they occur.

Stuck on c, any help would really be appreciated.
Reply 1
Avatar for Becca_1993
Becca_1993
to get the minimum and maximum you will have to differentiate your equation.

have the differenentiated equation =0 then calculate the value of θ

Then you can work out the y value of that point by inserting your calculated θ back into the original equation

If you want more help I can
(edited 11 years ago)
Reply 2
Avatar for cowshi
cowshi
OP
How do I differentiate 1/1+2secx?

Don;t think I have ever come across differentiating trig equations yet.
Reply 3
Avatar for Becca_1993
Becca_1993
There is a way of using a) and b) to help you but i can't think of how


When you differentiate sinx , you get cosx
When you differentiate cosx , you get -sinx
so when you differentiate -sinx , you get -cosx
and -cosx , to get sinx
Reply 4
Avatar for Jam'
Jam'
15
The minimum of 1+2secx is 3, so the maximum of 1/(1+2secx) is 1/3

The maximum of 1+2secx is -1, so the minimum of 1/(1+2secx) is 1/-1=-1

Now use your graph-drawing ability and understanding of periodicity to deduce at what values of theta these occur at.
Reply 5
Avatar for cowshi
cowshi
OP
Had another look at my graph and I have it.

Just put the pi and 2pi into my equation and I think I'm getting the right answer.

Appreciate the help

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