A bit of help please! (1 Viewer)

[Makematics]

did u use complementary angles to solve?

yep. i think there should be four distinct solutions, but im getting heaps of solutions...

 

[HeroicPandas]

nvm made a mistake

 

[Sy123]

tried that before i posted narrowed it down to cos (3theta)=sin(4theta), which i solved using general solutions... and it didnt work out very well

There should be 8 solutions it seems from graphing them in geogebra



Now we use sum to product formula:



Which is easy enough to solve, for the first one:



Only solution in this domain then for the first sine, is

Now, for the second one:



Only solutions for this in the domain:



Hence

 

[Makematics]

hmmm ok those are what i got in the first place :/ it just didnt seem right Plus the answers had 4 solutions... Ok well thank you!

 

[RealiseNothing]

If you consider a right angled triangle with angles you will see the above holds true. Hence:

for





Sub in for your solutions.

Though you will have to manually test because we used a right angled triangle.

 

[RealiseNothing]

Hmm if that works that means you can do the general case of: