T formulae questions (1 Viewer)

[clintmyster]

Now you put that back in and factorise. You should get that.

you mean replace t now with t=7.5?

 

[clintmyster]

Yeah. On top, you should get cos^2(7.5) because 1-sin^2(x) = cos^2(x)
And on the bottom you should have sec^(x) because 1+tan^2(x) = sec^2(x).

the top should be like 4(tan 7.5)(1-tan^2(7.5)) right? can you guide me through it please? do you change the tan^2(7.5) to like sec^2(7.5) - 1 and proceed from there?

goshh do each question need this kind of working out? its huge!

 

[lolokay]

i know that but how do you use that in this scenario..i dont see many ways of making this in terms of sin unless you convert tan...is this question supposed to be hard? its supposedly the "easier" questions in yr12 3u!

the question is 2tan15/(1+tan^2 15) , and sin@ = 2t/(1+t^2), where t = tan @/2

so let tan @/2 = tan15, @ = 30

therefore 2tan15/(1+tan^2 15) = sin30 = 1/2

this is definitely an easy question since its just sub'ing into the t formula for sin@

 

[lyounamu]

the top should be like 4(tan 7.5)(1-tan^2(7.5)) right? can you guide me through it please? do you change the tan^2(7.5) to like sec^2(7.5) - 1 and proceed from there?

goshh do each question need this kind of working out? its huge!

I will do it again. I am a bit confused now. Because I am doing two questions simultaneously (from another thread).

 

[midifile]

i know that but how do you use that in this scenario..i dont see many ways of making this in terms of sin unless you convert tan...is this question supposed to be hard? its supposedly the "easier" questions in yr12 3u!

Rather than making t = tan (7.5) let t = tan 15.
therefore 2tan15/1+tan^2(15) = 2t/1+t^2
= sin(2x15) (using the sin t-formula)
= sin30
=1/2

 

[lyounamu]

the question is 2tan15/(1+tan^2 15) , and sin@ = 2t/(1+t^2), where t = tan @/2

so let tan @/2 = tan15, @ = 30

therefore 2tan15/(1+tan^2 15) = sin30 = 1/2

this is definitely an easy question since its just sub'ing into the t formula for sin@

I thought this question was supposed to be "prove". Damn! Why did I even go further when I didn't need to?

 

[clintmyster]

the question is 2tan15/(1+tan^2 15) , and sin@ = 2t/(1+t^2), where t = tan @/2

so let tan @/2 = tan15, @ = 30

therefore 2tan15/(1+tan^2 15) = sin30 = 1/2

this is definitely an easy question since its just sub'ing into the t formula for sin@

what im still not getting is why did you choose to sub the angle in sin @...why not cos? how did that come about?

 

[lyounamu]

what im still not getting is why did you choose to sub the angle in sin @...why not cos? how did that come about?

If you look at the question closely, it resembles

2t/(1+t^2)

where t = tan15 (which is tan 30/2)
Therefore, the answer is basically sin 30.

 

[clintmyster]

If you look at the question closely, it resembles

2t/(1+t^2)

where t = tan15 (which is tan 30/2)
Therefore, the answer is basically sin 30.

oh that makes a lot of sense now! does that mean for like 4f) it resembles tan and 3b,d) sine again?

 

[lyounamu]

oh that makes a lot of sense now! does that mean for like 4f) it resembles tan and 3b,d) sine again?

Yeah. I thought they were "prove" questions. Otherwise, they are just too simple that you only write like 2 lines and finish.

 

[lolokay]

I thought this question was supposed to be "prove". Damn! Why did I even go further when I didn't need to?

well, even if it was a prove question you could have made things easier by proving that sin@ = 2t/(1 + t^2). though wouldn't you be able to use the t identities in a proof?

 

[clintmyster]

Yeah. I thought they were "prove" questions. Otherwise, they are just too simple that you only write like 2 lines and finish.

i got proving ones coming up but like how hard could they be? this is my very last question i gotta do. just steps to guide me through it will be enough i think?

 

[midifile]

i got proving ones coming up but like how hard could they be? this is my very last question i gotta do. just steps to guide me through it will be enough i think?

on the lhs sub (1+t^2)/(2t) for cosec@ and 1-t^2/2t for cot@ and then get rid of the fractions by multiplying top and bottom by 2t. It should rearrange to (1+t)/(1-t)

 

[clintmyster]

i got the LHS alright but with the rhs do you sub in 2t/1-t^2 for tan1/2@?


edit: nevermind i am realy acting stupid today not seeing simple things like that tan1/2@ becomes t omgg...this is like the only trig i dont like LOLL..its in my way of a perfect score grrr!

 

[midifile]

i got the LHS alright but with the rhs do you sub in 2t/1-t^2 for tan1/2@?

No. t=tan (1/2@), so if you have (1+t)/(1-t), you can sub in t=tan(1/2@) which gives you 1+tan(1/2@)/1-tan(1/2@)

 

[lyounamu]

well, even if it was a prove question you could have made things easier by proving that sin@ = 2t/(1 + t^2). though wouldn't you be able to use the t identities in a proof?

Lol, ok.

Well, my brain is not functioning well today. I had an exam today, that's probably why.

 

[midifile]

edit: nevermind i am realy acting stupid today not seeing simple things like that tan1/2@ becomes t omgg...this is like the only trig i dont like LOLL..its in my way of a perfect score grrr!

Lol. Once you become confident with t-formulas youll be okay. When I first did them I was shit at those prove questions, but you just have to practice them and eventually it will become second nature.

 

[clintmyster]

No. t=tan (1/2@), so if you have (1+t)/(1-t), you can sub in t=tan(1/2@) which gives you 1+tan(1/2@)/1-tan(1/2@)

yeah i see all that now..s many mediocre mistakes in this...and its not even remotely challenging or hard to get my head around..maybe i dont feel like doing this or something

anyways guys thanks heaps for the help..clarified a few things for me which i didnt actually realise and yeah =]

 

[midifile]

Lol, ok.

Well, my brain is not functioning well today. I had an exam today, that's probably why.

What you were doing was right you just did it for the wrong question Hope your brain feels better tomorrow

 

[clintmyster]

Lol, ok.

Well, my brain is not functioning well today. I had an exam today, that's probably why.

was it a math exam? howd you go?