1. Urgent- trigonometry help?

Circle below has radius 1. Eight segment lengths are labeled with lowercase letters. Six of these equal a trigonometric function of . Your answer to this problem should be a six letter sequence whose letters represent the segment lengths that equal the following functions (in the correct order):So, for example, you would answer akhcbd if you thought , , , , , and .

Any ideas/directions/solutions greatly appreciated! Thanks!

2. Re: Urgent- trigonometry help?

do you know the definitions of any of these trig functions they are talking about?

If not why not? Is this for your class?

Go look up how all these trig functions are defined in terms of pieces of right triangles.

This should get you started.

3. Re: Urgent- trigonometry help?

Yeah, I got sin phi = d, cos=a, tan= d/a, csc = 1/d, sec= 1/a, and cot = a/d, but I'm not sure how to figure in the other letters!

4. Re: Urgent- trigonometry help?

I think the key is in triangle similarity, but I don't know exactly which are similar?

5. Re: Urgent- trigonometry help?

Originally Posted by orange
Yeah, I got sin phi = d, cos=a, tan= d/a, csc = 1/d, sec= 1/a, and cot = a/d, but I'm not sure how to figure in the other letters!
theta, not phi. phi looks like $\phi$

a couple minutes of toying with this shows it to be rather a pain.

What you've done so far looks good.

What I would try is to solve for the other angles of the various triangles in terms of theta.
Then compute the various trig functions using those new angles and appropriate sides.

For example. The far right angle is going to be 90-theta degrees (can you see why?)
now cos(90-theta) = sin(theta), and sin(90-theta)= cos(theta) (you should show this)

so sin(theta) = h/(a+b)
cos(theta) = 1/(a+b)

and thus tan(theta) = h/(a+b) / (1/(a+b)) = h!

and just keep chipping away at it.

good luck.

6. Re: Urgent- trigonometry help?

Thank you so much. Is that rightmost angle 90-theta because of similarity to the triangle beside it (that shares side d and the right angle?)

Also am I correct in surmising the top left-most corner is also theta?

7. Re: Urgent- trigonometry help?

well let's see

you know the angle adjacent to theta is 90-theta, because the two of them make up that bottom left right angle.
Then the angle opposite that is 90 deg as drawn. So the top left angle must be 180 - (90-theta) - (90) = theta.

so yes you are correct.

8. Re: Urgent- trigonometry help?

So far as finding cotan, I'm guessing it's something to do with the Sine Law since 1/h is sin(90)/h in that triangle. So 1/h = (sin theta)/b = d/b, which is also cos(90-theta), thus cos(theta) and so d/b=a/d and d^2=ab

9. Re: Urgent- trigonometry help?

So I can rewrite a as d^2/b. Now cot theta is a/d, so that becomes d^2/b \div b = d^2

And I know d^2 is 1-a^2?

10. Re: Urgent- trigonometry help?

you understand it all. You don't need me to cheerlead you on. Just keep hacking away at it.

11. Re: Urgent- trigonometry help?

Alright, thank you!