## anonymous one year ago Write the following as an algebriac expression in "x" cot(arccos(3x)), 0 ≤ x ≤ 1/3

1. misty1212

HI!!

2. anonymous

This problem makes my head hurt :( lol

3. misty1212

this is really not that bad at all first step: draw a triangle with some angle $$\theta$$ labelled next step, since $\cos(\theta)=3x$ put a $$3x$$ on the "adjacent" side and make the hypotenuse 1

4. misty1212

|dw:1434129152248:dw|

5. misty1212

there is a picture of an angle whose cosine is $$3x$$ what you need is the "opposite" side which you find via pythagoras

6. misty1212

let me know what you get it should have a square root in it

7. anonymous

:o let me try

8. anonymous

sqrt(-9x^2 + 1) ?

9. misty1212

yes although $\sqrt{1-9x^2}$ looks neater

10. anonymous

haha alright

11. misty1212

now you want the cotangent of that angle, which is "adjacent over opposite" so you are pretty much done, just write it i

12. anonymous

Yeah I got it form here, you just made that so easy it's ridiculous. Thank you so much

13. misty1212

it is ridiculously easy if you know what you are doing hope your head does not hurt anymore $\color\magenta\heartsuit$

14. anonymous

It's alleviated :)