Lots to catch up on, and over the week-end I’ll begin updating the posts with solutions people have provided, but let’s keep things rolling.
Below are the final three questions from the 1913 Matric trigonometry Honours exam. This follows on from TNDOT 13 and TNDOT 14, and noting Q7 below has already appeared (and solved), as TNDOT 4. As background, the other trig TNDOT posts are TNDOT 1, TNDOT 2 and TNDOT 8.
Have fun.
7. From the equations
(i) Eliminate 
and express the result in a simple form;
(ii) Find 
and 
in terms of .
8. How can the height of an object be obtained by observing angles at two stations of known height?
Shew that this method fails when the two stations are on the same level.
9. Define the terms side and angle of a spherical triangle.
If 
, 
and 
are the angles and 
, 
and 
the sides of a spherical triangle, obtain an expression for 
in terms of trigonometrical ratios of , and .
The sides of an isosceles spherical triangle are , and , and the vertical angle . Prove that
“Lot’s”
Jesus. “Don’t drink and blog.” Thanks. Fixed.
Know your limits…
…study calculus.
Off topic, but do you have any advice on continuing studying maths (as a hobby) now that I’m finished VCE?
(For example, do you know any good Math textbooks that I can work through in my free time)
Hi Jay. Maybe email me and we can chat offline.
I have a solution for Q7 but it is a bit long… 3 pages of handwritten notes.
Maybe I’ve missed a short-cut!
Geez, your homework is very late. (But at least you got it in.)
Q7 was solved as TNDOT 4. I’m not sure one can do much better than that.
Yeah, I forgot about that discussion…
I played around with the Cramer’s rule idea a bit since and decided that it works but is probably not an improvement on other solutions.
I never learnt the spherical triangles stuff properly myself so will admit to skipping over those questions.