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# Core 3 Functions Question

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1. Hi,

I'm doing exercise 1C from the core 3 and 4 aqa book and have got stuck on question 8.
It says f(x)=/tan2x/ where / represents the modulus line
Solve f(x)=/tan2x/=1 for -90degrees </= x </= +90degrees

I get the +/- 22.5 degrees but I don't understand how they also get +/- 67.5 degrees.

Any help would be greatly appreciated.
2. (Original post by Blake Jones)
Hi,

I'm doing exercise 1C from the core 3 and 4 aqa book and have got stuck on question 8.
It says f(x)=/tan2x/ where / represents the modulus line
Solve f(x)=/tan2x/=1 for -90degrees </= x </= +90degrees

I get the +/- 22.5 degrees but I don't understand how they also get +/- 67.5 degrees.

Any help would be greatly appreciated.

Remember that if then or .
3. The problem you have is that when you get 2x=+-45 degrees you also have 2x=+-135 degrees (tan function, add/subtract 180) which gives you +-67.5 degrees for x. It's helpful to use a CAST diagram and to rewrite your bounds as -180<=2x<=180
4. Well you would get . That solves but you also have which solves .
These are general solutions but you just plug values of n in so that the solutions fall in the domain specified. Remember that the tangent function is periodic with a period of 180 degrees.
5. (Original post by Bananapeeler)
The problem you have is that when you get 2x=+-45 degrees you also have 2x=+-135 degrees (tan function, add/subtract 180) which gives you +-67.5 degrees for x. It's helpful to use a CAST diagram and to rewrite your bounds as -180<=2x<=180
Ah thank you! I added/subtracted 180 from the 22.5 not the original!

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