Hello,

I am a tad stuck on this question, so any help would be welcome.

y = (2x – 1)Tan 2x

Has a minimum Turing point at P, the x co-ordinate of P is K

Show that K satisfies the following

4K + sin 4K -2 = 0

thank you for the help

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- Apr 15th 2007, 09:40 AMsillyhackertrigonometry equation
**Hello,**

**I am a tad stuck on this question, so any help would be welcome.**

**y = (2x – 1)Tan 2x**

**Has a minimum Turing point at P, the x co-ordinate of P is K**

**Show that K satisfies the following**

**4K + sin 4K -2 = 0**

**thank you for the help**

- Apr 15th 2007, 11:02 AMtopsquark
Take the first derivative:

y = (2x - 1)*tan(2x)

y' = 2*tan(2x) + (2x - 1)* sec^2(2x)*2

At the minimum point y' = 0, so given the x = K:

2*tan(2K) + (2K - 1)* sec^2(2K)*2 = 0

Now, tan(2k) = sin(2K)/cos(2K) and sec(K) = 1/cos(K), so:

2*sin(2K)/cos(2K) + 2*(2K - 1)/cos^2(2K) = 0

Now multiply both sides by cos^2(2K):

2*sin(2K)*cos(2K) + 2*(2K - 1) = 0

But 2*sin(2K)*cos(2K) = sin(4K), so

sin(4K) + 4K - 2 = 0

which is your relationship.

-Dan