Presto
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I don't understand any of this :sigh::sad:
Could someone pls explain?
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RDKGames
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(Original post by I-try)
I don't understand any of this :sigh::sad:
Could someone pls explain?
\tan(x-40)=1.5 and you're solving for x. Obviously the first step is to get rid off the tan by inverse tanning both sides to get x-40 = 56.3 then add on the 40 to get the first answer. This isn't the only solutions obviously because tan is periodic and it repeats itself every 180 degrees, hence the solution x-40 = 56.3-180 is also valid which is where the second solution of x=-83.7 comes from.

Part (ii) is just using some basic algebraic manipulation and identities you should know in order to express the equation entirely in terms of \cos \theta. Not sure what's confusing in their solution.

Then solving \sin \theta \tan \theta = 3 \cos \theta + 2 is the same as solving the quadratic you just derived since all the solutions will be exactly the same because all you do is just manipulate the eq. into a different form. It's the difference between solving (x+2)(x-1)=0 and x(x+1)=2.
Once it comes to the \cos \theta = ... at the end, all you need to be aware of is that cosine repeats itself every 360 degrees so we can use the same trick as we do with tan and just subtract/add 360 rather than 180 to get further solutions.

If it's the theory behind it you don't understand then TSR is not the best place to ask for help on that.
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Presto
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I didn't get your explanation when I first read it so I watched a few vids on trig identities and eqs, then returned to this and what you said makes perfect sense now. Thank you, really helpful
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